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Similar Question 1
<p>Determine the equation of a parabola that has its axis parallel to the y-axis and passes through the points <code class='latex inline'>(-1, 2), (1, -1)</code>, and <code class='latex inline'>(2, 1)</code>. (Note that the general form of the parabola that is parallel to the y-axis is <code class='latex inline'>y = ax^2 + bx + c</code>.)</p>
Similar Question 2
<p>Use the graph of each quadratic relation to determine the roots to each quadratic equation, where <code class='latex inline'>y=0</code>.</p><img src="/qimages/856" />
Similar Question 3
<ol> <li>Sketch the graphs of the following quadratic functions by factoring to locate the <code class='latex inline'> x </code> -intercepts, and then finding the coordinates of the vertex.</li> </ol> <p><code class='latex inline'>\displaystyle y=x^{2}+2 x-8 </code></p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p> Write each function in the form <code class='latex inline'> y=(x-h)^{2}+k . </code> Then, graph the function. Show the coordinates of the vertex and the equation of the axis of symmetry. State the range.</p><p><code class='latex inline'>\displaystyle y=-4 x^{2}+8 x-7 </code></p>
<p>Determine the maximum or minimum of each function.</p><p><code class='latex inline'>\displaystyle g(x)=-2 x^{2}+x+15 </code></p>
<p>Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y=x^{2}-12 x+36 </code></p>
<p>Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.</p><p><code class='latex inline'>\displaystyle y = -x^2 -6x + 27 </code></p>
<p>Write each function in the form <code class='latex inline'> y=(x-h)^{2}+k </code> . Then, graph the function. Show the coordinates of the vertex and the equation of the axis of symmetry. State the range.</p><p><code class='latex inline'>\displaystyle y=2 x^{2}-4 x+5 </code></p>
<p>Express each function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex without graphing.</p><p><code class='latex inline'>\displaystyle g(x)=-6 x^{2}+24 </code></p>
<p>Without graphing, determine the number of x-intercepts that the relation has.</p><p><code class='latex inline'>\displaystyle y = 2x^2 + 8x + 14 </code></p>
<p>Determine the exact values of the</p><p><code class='latex inline'>\displaystyle x </code>-intercepts of each quadratic function. Use a graphing calculator to check that</p><p>you have found the correct number of</p><p><code class='latex inline'>\displaystyle x </code>-intercepts.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}+5 x+1 </code></p>
<p>Sketch the graphs of the following quadratic functions by factoring to find the <code class='latex inline'> x </code> -intercepts, and then deducing the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}+4 x-5 </code></p>
<p>Find the x-intercepts, the vertex, and the axis of symmetry of each quadratic relation. Then, sketch the graph of the parabola.</p><p><code class='latex inline'>y=3x^2-14x-5</code></p>
<p>Discuss how the graph of the quadratic relation <code class='latex inline'>y = 4x^2 + bx + 6</code> changes as <code class='latex inline'>a, b</code>, and <code class='latex inline'>c</code> are changed.</p>
<p> Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=-x^{2}-4 x-7 </code></p>
<p>Find the value(s) of <code class='latex inline'>b</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p><code class='latex inline'>y=25x^2-30x+b</code></p>
<p>Which quadratic relations have x = 3 as the axis of symmetry?</p><p>A. <code class='latex inline'>y = 4(x -3)^2 + 6</code></p><p>B. <code class='latex inline'>y = -2(x -5)(x -1)</code></p><p>C. <code class='latex inline'>y = x^2 - 6x + 7</code></p><p>D. All of the above</p>
<p>Use technology to graph each quadratic relation below. Then determine</p> <ul> <li>i) the equation of the axis of symmetry</li> <li>ii) the coordinates of the vertex</li> <li>iii) the y-intercept</li> <li>iv) the zeros</li> <li>v) the maximum or minimum value</li> </ul> <p> <code class='latex inline'>y=x^2-4x+3</code></p>
<p> Determine the y—intercept, zeros, equation of the axis of symmetry, and vertex.</p><p><code class='latex inline'>\displaystyle y = x^2 + 8x + 15 </code></p>
<p>Rewrite the relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. </p><p>Graph the relation and give the vertex and the equation of the axis of symmetry.</p><p><code class='latex inline'>\displaystyle y = x^2 +4x + 1 </code></p>
<p>Casey completed the square to write <code class='latex inline'>y = 2x^2 - 6x + 5 </code> in vertex form. ls his solution correct or incorrect? If incorrect, identify the error and show the correct solution.</p><img src="/qimages/2087" />
<p>Without graphing, determine the number of zeros that each relation has.</p><p><code class='latex inline'>y=-2x^2+3x-7</code></p>
<p>Find the value(s] of k so that the parabola has only one x-intercept.</p><p><code class='latex inline'>\displaystyle y = -4x^2 + 28x + k </code></p>
<p>Write in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle f(x) = \frac{1}{2}x^2 -6x +26 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=40-12 x+x^{2} </code></p>
<p>Determine whether each quadratic function intersects the <code class='latex inline'>x</code>—axis at one point, two points, or not at all. Do not draw the graph.</p><p><code class='latex inline'>f(x)=3x^2+6x-1</code></p>
<p>Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = x^2 - 14x + 50 </code></p>
<ol> <li>Sketch the graphs of the following</li> </ol> <p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}+10 x+21 </code></p>
<p>Use partial factoring to determine the vertex of each function. State if the vertex is a minimum or a maximum.</p><p> <code class='latex inline'>\displaystyle f(x)=6 x^{2}-6 x-\frac{3}{2} </code></p>
<p>Graph each function to find the zeros. Rewrite the function with the polynomial in factored form.</p><p><code class='latex inline'>\displaystyle y = 2x^2 + 3x - 5 </code></p>
<p>Determine the maximum or minimum value for each quadratic function.</p><p><code class='latex inline'>\displaystyle g(x)=4 x^{2}+4 x-3 </code></p>
<p>Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=x^{2}-4 x-1 </code></p>
<p>Determine the equation of the quadratic function <code class='latex inline'>f(x) = ax^2 - 6x - 7</code> if <code class='latex inline'>f(2) = 3</code>.</p>
<p>Create a table of values for each quadratic relation, and sketch its graph. Then determine</p> <ul> <li>i) the equation of the axis of symmetry</li> <li>ii) the coordinates of the vertex</li> <li>iii) the y-intercept</li> <li>iv) the zeros</li> <li>v) the maximum or minimum value</li> </ul> <p><code class='latex inline'>y=x^2-2x+1</code></p>
<p>Andrew thinks that the quadratic function <code class='latex inline'>f(x)=x^2-5x+2</code> does not intersect the <code class='latex inline'>x</code>-axis because the discriminant is negative. Do you agree? Explain.</p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=2 x^{2}+4 x+3 </code></p>
<p>Graph each function.</p><p><code class='latex inline'>\displaystyle f(x)=-\frac{1}{2} x^{2}-4 x-4 </code></p>
<p>Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=-x^{2}-8 x-7 </code></p>
<p>Compare the axis of symmetry of</p><p><code class='latex inline'>\displaystyle y = 3x^2+18x -17 </code> to that of <code class='latex inline'>\displaystyle y = 3x^2 + 18x +1 </code>. Explain your findings. </p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-0.5 x^{2}+3 x-5 </code></p>
<p>Rewrite the relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. </p><p>Graph the relation and give the vertex and the equation of the axis of symmetry.</p><p><code class='latex inline'>\displaystyle y = 3 - 4x -x^2 </code></p>
<p>Express each function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex without graphing.</p><p><code class='latex inline'>\displaystyle g(x)=2 x^{2}-13 x-7 </code></p>
<p>Write in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle f(x) = -x^2 + 8x - 7 </code></p>
<p>A quadratic relation can be expressed in three ways: standard form, factored form, and vertex form. In which set(s) of equations is a quadratic relation correctly written in all three forms?</p><p>Set 1: <code class='latex inline'>\displaystyle \begin{aligned} y &=-2 x^{2}+8 x+10 \\ y &=-2(x+1)(x-5) \\ y &=-2(x-2)^{2}+18 \\ \text { Set 2: } & y=3 x^{2}+9 x-84 \\ y &=3(x+7)(x-4) \\ y &=3(x+1.5)^{2}-88.5 \end{aligned} </code></p><p><code class='latex inline'>\displaystyle \begin{array}{ll}\text { A. } \text { set } 1 \text { only } & \text { C. neither set } \\ \text { B. } \operatorname{set} 2 \text { only } & \text { D. both sets }\end{array} </code></p>
<p>Consider the relation <code class='latex inline'>\displaystyle y = -3x^2 -12x -2 </code></p><p>a) Write the relation in vertex form by completing the square.</p><p>b) State the transformations that must be applied to <code class='latex inline'>y =x^2</code> to draw the graph of the relation.</p><p>c) Graph the relation.</p>
<p>Find the value(s) of <code class='latex inline'>n</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p> <code class='latex inline'>y=16x^2-8x+n</code></p>
<p>Find the value(s) of <code class='latex inline'>n</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p><code class='latex inline'>y=-x^2+nx-9</code></p>
<p>Could you</p><p>use the above method for</p><p>sketching the graph of</p><p><code class='latex inline'>\displaystyle y=a x^{2}+b x+c </code> when <code class='latex inline'>\displaystyle a x^{2}+b x+c </code> is a perfect square? Explain.</p>
<p>Determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>b</code> in the relation <code class='latex inline'>y=ax^2+bx+7</code> if the vertex is located at (4,-5).</p>
<p>Find <code class='latex inline'>\displaystyle f(3) </code> for each function. Sketch a graph of each function.</p><p><code class='latex inline'>\displaystyle f(x)=4 x^{2}-12 x+9 </code></p>
<p>Determine the maximum or minimum of each function.</p><p><code class='latex inline'>\displaystyle g(x)=-2 x^{2}-6 x+36 </code></p>
<p>Write each quadratic relation in vertex form using an appropriate strategy.</p><p><code class='latex inline'>\displaystyle y = -2x^2 + 12x - 11 </code></p>
<p>A parabola passes through points <code class='latex inline'>(3,0), (7,0)</code>, and <code class='latex inline'>(9,-24)</code>.</p> <ul> <li>Write the equation in standard form.</li> </ul>
<p>A parabola has equation <code class='latex inline'>y=9x^2+x+h.</code> One x-intercept is <code class='latex inline'>-2</code>. What is the value of <code class='latex inline'>h</code>?</p>
<p>Find the value(s) of <code class='latex inline'>b</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p><code class='latex inline'>y=4x^2+bx+9</code></p>
<ol> <li>Communication The <code class='latex inline'>\displaystyle x </code>-intercepts of a parabola are 5 and <code class='latex inline'>\displaystyle -7 . </code> What is the equation of the axis of symmetry? Explain.</li> </ol>
<p>Determine the maximum or minimum of each function.</p><p><code class='latex inline'>\displaystyle g(x)=-2 x^{2}+x+15 </code></p>
<p> Determine the exact values of the</p><p><code class='latex inline'>\displaystyle x </code>-intercepts of each quadratic function. Use a graphing calculator to check that</p><p>you have found the correct number of</p><p><code class='latex inline'>\displaystyle x </code>-intercepts.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}-6 x+7 </code></p>
<p>Find the x-intercepts of the parabola.</p><p><code class='latex inline'>\displaystyle y = 4x^2 -12x + 9 </code></p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=0.5 x^{2}+x+2 </code></p>
<p>Determine the vertex, the axis of symmetry, the direction the parabola opens, and the number of zeros for each quadratic function. Sketch a graph of each.</p><p><code class='latex inline'> \displaystyle f(x) = -x^2 + 16x -64 </code></p>
<p>A quadratic function has equation <code class='latex inline'>f(x)=x^2-x-6</code>. Determine the x-intercepts for each function.</p><p><code class='latex inline'> \displaystyle \begin{array}{cccccc} &(a)& y = f(2x) &(b)& y=f(\frac{1}{3}x) &(c) & y=f(-3x) \\ \end{array} </code></p>
<p>Explain what must be true for a parabola to have only one <code class='latex inline'>x</code>-intercept.</p>
<p>For which quadratic function is <code class='latex inline'>\displaystyle -3 </code> the constant term? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { A } y=(3 x+1)(-x-3) & \text { (C) } f(x)=(x-3)(x-3) \ \text { (B) } y=x^{2}-3 x+3 & \text { D) } g(x)=-3 x^{2}+3 x+9\end{array} </code></p>
<p>Write in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle f(x) = 2x^2 + 2x +4 </code></p>
<p>Determine the values of <code class='latex inline'>a</code> and <code class='latex inline'>b</code> in the relation <code class='latex inline'>y=ax^2+bx+8</code> if the vertex is located at (1,7).</p>
<p>Write each function in the form <code class='latex inline'> y=(x-h)^{2}+k </code> . Then, graph the function. Show the coordinates of the vertex and the equation of the axis of symmetry. State the range.</p><p><code class='latex inline'>\displaystyle y=3 x^{2}+6 x-8 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=x^{2}-2 x-8 </code></p>
<p>Determine the equation of the axis of symmetry of a parabola that passes through points <code class='latex inline'>(2, 8)</code> and <code class='latex inline'>(-6,8)</code>.</p>
<ol> <li>Sketch the graphs of the following quadratic functions by factoring to locate the <code class='latex inline'> x </code> -intercepts, and then finding the coordinates of the vertex.</li> </ol> <p><code class='latex inline'>\displaystyle y=x^{2}+2 x-8 </code></p>
<p>Determine the equation of a parabola that has its axis parallel to the y-axis and passes through the points <code class='latex inline'>(-1, 2), (1, -1)</code>, and <code class='latex inline'>(2, 1)</code>. (Note that the general form of the parabola that is parallel to the y-axis is <code class='latex inline'>y = ax^2 + bx + c</code>.)</p>
<p>A parabola passes through points <code class='latex inline'>(3,0), (7,0)</code>, and <code class='latex inline'>(9,-24)</code>.</p> <ul> <li>Determine the coordinates of the vertex, and write the equation in vertex form.</li> </ul>
<p>Describe how you would sketch the graph of <code class='latex inline'>\displaystyle f(x)=2 x^{2}-4 x-30 </code> without using a table of values.</p>
<p>Without solving, determine the number of real roots it has.</p><p><code class='latex inline'>y = 2x^2 -4x + 7</code></p>
<p>Determine the number of zeros of the function <code class='latex inline'>f(x) = 4-(x-3)(3x + 1)</code> without solving the related quadratic equation or graphing. Explain.</p>
<ol> <li>Sketch the graphs of the following</li> </ol> <p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}-2 x-35 </code></p>
<p>State whether you agree or disagree with each statement. Explain why.</p> <ul> <li>All quadratic relations of the form <code class='latex inline'>y=ax^2+bx+c</code> have two zeros.</li> </ul>
<p>Use technology to graph each quadratic relation below. Then determine</p> <ul> <li>i) the equation of the axis of symmetry</li> <li>ii) the coordinates of the vertex</li> <li>iii) the y-intercept</li> <li>iv) the zeros</li> <li>v) the maximum or minimum value</li> </ul> <p> <code class='latex inline'>y=-x^2+6x-5</code></p>
<p> The six graphs represent the six equations <code class='latex inline'> y=x^{2}+4 x, y=x^{2}-4 x </code> <code class='latex inline'> y=-x^{2}+4 x, y=-x^{2}-4 x, y=x^{2}-4 </code> , and <code class='latex inline'> y=-x^{2}+4 . </code> Match each graph with the correct equation.</p><img src="/qimages/64162" />
<p>Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y=4-6 x-x^{2} </code></p>
<p>Graph each quadratic function by hand by determining the zeros, vertex, axis of symmetry, and <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle g(x)=2 x^{2}+2 x-12 </code></p>
<p>For <code class='latex inline'>f(x) = x^2 -4x +1</code>, find</p><p>the coordinates of point <code class='latex inline'>B</code>, where <code class='latex inline'>x =5</code></p>
<ol> <li>Sketch the graphs of the following quadratic functions by factoring to locate the <code class='latex inline'> x </code> -intercepts, and then finding the coordinates of the vertex.</li> </ol> <p><code class='latex inline'>\displaystyle y=x^{2}-4 x+3 </code></p>
<img src="/qimages/2494" /><p>The equation of one of these parabolas is shown <code class='latex inline'>y=x^2-8x+18</code>. Determine the equation of the other in vertex form.</p>
<p>a) Graph the following relations by developing a table of values and plotting points. Then, find the first and second differences. </p><p><code class='latex inline'>\displaystyle \begin{array}{lllll} &y = x^2 -4x \\ &y = x^2 -4x + 5 \\ &y = x^2 -4x -2 \end{array} </code></p><p>b) Examine each graph and use its properties to write an equation in the form <code class='latex inline'>y=(x-h)^2+k</code>.</p><p>c) What conclusions can you make about the relation <code class='latex inline'>y = x^2 - 4x + c</code> for different values of <code class='latex inline'>0</code>?</p>
<p>Express each quadratic function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}-7 x+12 </code></p>
<p>A parabola has a y-intercept of <code class='latex inline'>5</code> and contains the points <code class='latex inline'>(3,1)</code> and <code class='latex inline'>(-1,15)</code>. What are the coordinates of the vertex?</p>
<p>Which equation is equivalent to</p><p><code class='latex inline'>\displaystyle y=x^{2}+6 x+7 ? </code></p><p>A. <code class='latex inline'>\displaystyle y=(x+6)^{2}-2 \quad </code> C. <code class='latex inline'>\displaystyle y=(x+3)^{2}-2 </code></p><p>B. <code class='latex inline'>\displaystyle y=(x+3)^{2}+7 \quad </code> D. <code class='latex inline'>\displaystyle y=(x+3)^{2}-6 </code></p>
<ol> <li>Sketch the graphs of the following quadratic functions by factoring to locate the <code class='latex inline'> x </code> -intercepts, and then finding the coordinates of the vertex.</li> </ol> <p><code class='latex inline'>\displaystyle y=x^{2}-2 x-15 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=x^{2}+4 x </code></p>
<p>Write in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle f(x) = 2x^2 + 20x +16 </code></p>
<p>Express each function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex without graphing.</p><p><code class='latex inline'>\displaystyle g(x)=3 x^{2}+12 x-15 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=10 x-25-x^{2} </code></p>
<p>Match each function to its graph.</p><p>a) <code class='latex inline'>\displaystyle f(x)=x^{2}+7 x+10 </code></p><p>b) <code class='latex inline'>\displaystyle f(x)=(5-x)(x+2) </code></p><p>c) <code class='latex inline'>\displaystyle f(x)=-x^{2}+3 x+10 </code></p><p>d) <code class='latex inline'>\displaystyle f(x)=(x+2)(x+5) </code></p><p>e) <code class='latex inline'>\displaystyle f(x)=x^{2}-3 x-10 </code></p><img src="/qimages/164651" />
<p>Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=12-8 x+x^{2} </code></p>
<p>Esther claims that the standard form of a quadratic relation is best for solving problems where you need to determine the maximum or minimum value, and that they vertex form is best to use to determine a parabola&#39;s zeros. Do you agree or disagree? Explain.</p>
<ol> <li>Communication a) On the same set of axes, graph the functions <code class='latex inline'>\displaystyle y=x </code> and <code class='latex inline'>\displaystyle y=x^{2} </code>, where <code class='latex inline'>\displaystyle x </code> and <code class='latex inline'>\displaystyle y </code> are real numbers. b) For the graph of <code class='latex inline'>\displaystyle y=x </code>, does <code class='latex inline'>\displaystyle x </code> or <code class='latex inline'>\displaystyle y </code> have a maximum or minimum value? Explain. c) For the graph of <code class='latex inline'>\displaystyle y=x^{2} </code>, does <code class='latex inline'>\displaystyle x </code> or <code class='latex inline'>\displaystyle y </code> have a maximum or minimum value? Explain. d) Describe any other similarities and differences in the graphs.</li> </ol>
<p>Explain why the condition <code class='latex inline'>a \neq 0</code> must be stated to ensure that <code class='latex inline'>y = ax^2 + bx + c</code> is a quadratic relation.</p>
<p>Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=28+12 x+x^{2} </code></p>
<p> State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=0.1 x^{2}+2 x+1 </code></p>
<p>Write in standard form the equation of the parabola passing through the given points.</p><p><code class='latex inline'>\displaystyle (-5,-8),(4,-8),(-3,6) </code></p>
<p> Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y-21=x^{2}-14 x </code></p>
<p>Graph each function, and then use the graph to locate the zeros.</p><p><code class='latex inline'>\displaystyle g(x)=2 x^{2}-3 x-5 </code></p>
<p> State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-0.003 x^{2}+0.6 x-10 </code></p>
<p>Determine the maximum or minimum of each function.</p><p> <code class='latex inline'>\displaystyle f(x)=x^{2}-2 x-35 </code></p>
<p>Write the function in vertex form.</p><p><code class='latex inline'> \displaystyle f(x) = 2x^2 + 3x + 1 </code></p>
<p>Write each function in the form <code class='latex inline'> y=(x-h)^{2}+k </code> . Then, graph the function. Show the coordinates of the vertex and the equation of the axis of symmetry. State the range.</p><p><code class='latex inline'>\displaystyle y=-3 x^{2}+12 x-14 </code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=\frac{1}{4} x^{2}+3 x+10 </code></p>
<ol> <li>Sketch the graphs of the following</li> </ol> <p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}-2 x-3 </code></p>
<p>Find the value(s) of <code class='latex inline'>n</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p> <code class='latex inline'>y=x^2+nx+25</code></p>
<p>State whether you agree or disagree with each statement. Explain why.</p> <ul> <li>All quadratic relations of the form <code class='latex inline'>y=ax^2+bx+c</code> have one y-intercept.</li> </ul>
<p>Find the x-intercepts of the parabola.</p><p><code class='latex inline'>\displaystyle y = x^2 -4x + 4 </code></p>
<p>Write the function in vertex form.</p><p><code class='latex inline'> \displaystyle f(x) = -x^2 + 3x - 2 </code></p>
<p>Graph each quadratic function by hand by determining the zeros, vertex, axis of symmetry, and <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}-x-20 </code></p>
<p>Write the quadratic equation <code class='latex inline'>y = 3x^2 - 30x + 73</code> in vertex form.</p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=5 x^{2}-20 x+18 </code></p>
<p> Determine the y—intercept, zeros, equation of the axis of symmetry, and vertex.</p><p><code class='latex inline'>\displaystyle y = -2x^2 + 16x -32 </code></p>
<p>The graph of the function <code class='latex inline'>\displaystyle y=x^{2}+5 x+6 </code> is shown at the right.</p><p>a. What are the <code class='latex inline'>\displaystyle x </code> -intercepts?</p><p>b. Factor <code class='latex inline'>\displaystyle x^{2}+5 x+6 </code>.</p><p>c. Reasoning Describe the relationship between the binomial factors you found in part (b) and the <code class='latex inline'>\displaystyle x </code> -intercepts.</p><img src="/qimages/74375" />
<p>Consider the relation <code class='latex inline'>y = -4x^2 + 40x - 91</code>.</p><p>a. Complete the square to write the equation in vertex form.</p><p>b. Determine the vertex and the equation of the axis of symmetry.</p><p>c. Graph the relation.</p>
<p>Find the x-intercepts, axis of symmetry, and vertex of each parabola. Then, graph the relation, labelling it fully.</p><p><code class='latex inline'>\displaystyle y = x^2 -10x + 25 </code> </p>
<p>Express each function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex without graphing.</p><p><code class='latex inline'>\displaystyle g(x)=x^{2}+10 x+21 </code></p>
<p>Determine the zeros of each function.</p><p><code class='latex inline'> \displaystyle g(x) = 2(x + 5)^2 - 98 </code></p>
<p>Write each function in vertex form, and then sketch its graph.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}+12 x-3 </code></p>
<ol> <li>Sketch the graphs of the following</li> </ol> <p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}-8 x </code></p>
<p>Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y=x^{2}+6 x+2 </code></p>
<p>Find the x-intercepts of the parabola.</p><p><code class='latex inline'>\displaystyle y =x^2 + 6x + 5 </code></p>
<p>Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.</p><p><code class='latex inline'>\displaystyle y = x^2 -4x -5 </code></p>
<p>Write the function in vertex form.</p><p><code class='latex inline'> \displaystyle f(x) = x^2 -12x + 35 </code></p>
<p>Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y=10 x-28-x^{2} </code></p>
<p>Create a table of values for each quadratic relation, and sketch its graph. Then determine</p> <ul> <li>i) the equation of the axis of symmetry</li> <li>ii) the coordinates of the vertex</li> <li>iii) the y-intercept</li> <li>iv) the zeros</li> <li>v) the maximum or minimum value</li> </ul> <p> <code class='latex inline'>y=-x^2-2x+3</code></p>
<p>The graph of the quadratic function <code class='latex inline'>y = ax^2 + bx + 1</code> passes through the point <code class='latex inline'>(1, 2)</code>. For what values of <strong>a</strong> does the graph of <code class='latex inline'>f(x)</code> intersect the x-axis at two distinct points?</p>
<ol> <li>Substitute the <code class='latex inline'>\displaystyle x </code>-coordinate of the vertex in <code class='latex inline'>\displaystyle y=x^{2}-2 x-8 </code> to find the <code class='latex inline'>\displaystyle y </code>-coordinate of the vertex.</li> </ol>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-2 x^{2}+20 x-44 </code></p>
<p>Determine the zeros and the maximum or minimum value for each function.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}+7 x+3 </code></p>
<p>What does <code class='latex inline'>a</code> in the equation <code class='latex inline'>y = ax^2 + bx + c</code> tell you about the parabola?</p>
<p>Sketch the graphs of the following quadratic functions by factoring to locate the <code class='latex inline'> x </code> -intercepts, and then finding the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}+6 x+8 </code></p>
<p> State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-4 x^{2}-24 x-29 </code></p>
<p>Graph each function, and then use the graph to locate the zeros.</p><p><code class='latex inline'>\displaystyle g(x)=15 x^{2}-2 x-1 </code></p>
<p>Determine whether a quadratic model exists for each set of values. If so, write the model.</p><p><code class='latex inline'>\displaystyle \left(-1, \frac{1}{2}\right),(0,2),(2,2) </code></p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-2.5 x^{2}+20 x-35 </code></p>
<p>Write in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle f(x) = x^2 + 2x - 15 </code></p>
<p>Write the function in vertex form.</p><p><code class='latex inline'> \displaystyle f(x) = -x^2 +6x + 7 </code></p>
<p>Write each quadratic relation in vertex form using an appropriate strategy.</p><p><code class='latex inline'>\displaystyle y = x^2 -6x- 8 </code></p>
<p> Determine the exact values of the</p><p><code class='latex inline'>\displaystyle x </code>-intercepts of each quadratic function. Use a graphing calculator to check that</p><p>you have found the correct number of</p><p><code class='latex inline'>\displaystyle x </code>-intercepts.</p><p> <code class='latex inline'>\displaystyle f(x)=\frac{3}{4} x^{2}-5 x+5 </code></p>
<p>State whether each parabola opens up or down.</p><p><code class='latex inline'> \displaystyle \begin{array}{cccccccc} &(a) & f(x) = 3x^2 & (c)& f(x) = -(x - 5)^2 -1 \\ &(b)& f(x) = -2(x - 3)(x + 1) &(d)& f(x) = \frac{2}{3}x^2 - 2x - 1 \\ \end{array} </code> </p>
<p>Determine the zeros and the maximum or minimum value for each function.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}+2 x-15 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=x^{2}-6 x+10 </code></p>
<p>Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.</p><p><code class='latex inline'>\displaystyle y = 3x^2 + 10x + 8 </code></p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-4 x^{2}+8 x-4 </code></p>
<ol> <li>Sketch the graphs of the following</li> </ol> <p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}-8 x+12 </code></p>
<p>Write each function in vertex form, and then sketch its graph.</p><p><code class='latex inline'>\displaystyle f(x)=-x^{2}-8 x-10 </code></p>
<p>Graph each quadratic function by hand by determining the zeros, vertex, axis of symmetry, and <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=-4 x^{2}-16 x+33 </code></p>
<p>Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=-x^{2}+8 x-11 </code></p>
<p>Sketch the graphs of the following</p><p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}-6 x+5 </code></p>
<p>Use technology to graph each quadratic relation below. Then determine</p> <ul> <li>i) the equation of the axis of symmetry</li> <li>ii) the coordinates of the vertex</li> <li>iii) the y-intercept</li> <li>iv) the zeros</li> <li>v) the maximum or minimum value</li> </ul> <p><code class='latex inline'>y=x^2+6x+8</code></p>
<p>Use partial factoring to determine the vertex of each function. State if the vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=\frac{2}{3} x^{2}+x+\frac{19}{8} </code></p>
<p>Express each quadratic function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}+5 x-3 </code></p>
<p>Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y=-x^{2}-4 x+1 </code></p>
<p>Locate the <code class='latex inline'>x</code>-intercepts of the graph of the function.</p><p><code class='latex inline'> \displaystyle f(x) = -4x^2 + 25x - 21 </code></p>
<p>Sketch the graphs of the following quadratic functions by factoring to find the <code class='latex inline'> x </code> -intercepts, and then deducing the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}+6 x+5 </code></p>
<ol> <li>If the function <code class='latex inline'>\displaystyle f(x)=a x^{2}+6 x+c </code> has no <code class='latex inline'>\displaystyle x </code>-intercepts, what is the mathematical relationship between <code class='latex inline'>\displaystyle a </code> and <code class='latex inline'>\displaystyle c </code> ?</li> </ol>
<p>Create a concept web that summarizes the different algebraic strategies you can use to determine the axis of symmetry and the vertex of a quadratic relation given in the form <code class='latex inline'>y=ax^2+bx+c</code>.</p>
<p>Rewrite the relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. </p><p>Graph the relation and give the vertex and the equation of the axis of symmetry.</p><p><code class='latex inline'>\displaystyle y = -x^2 - 6x - 5 </code></p>
<p>A parabola lies in only two quadrants. What does this tell you about the values of <code class='latex inline'>a, h</code> and <code class='latex inline'>k</code>. Explain your thinking, and provide the equation of a parabola as an example.</p>
<p>Write an equation in the form <code class='latex inline'>y = ax^2 + bx + c</code> to represent each parabola.</p><img src="/qimages/14069" />
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=1.5 x^{2}+6 x-8 </code></p>
<p>Write an equation, in the form <code class='latex inline'>y=ax^2+bx+c</code>, to represent each parabola.</p><p>c)</p><img src="/qimages/1113" />
<p>Match the factored form on the left with the correct standard form on the right. How did you decide on your answer? <code class='latex inline'>\displaystyle \begin{array}{ll}\text { a) } y=(2 x+3)(x-4) & \text { i) } y=4 x^{2}-19 x+12 \\ \text { b) } y=(4-3 x)(x+3) & \text { ii) } y=-3 x^{2}-5 x+12 \\ \text { c) } y=(3 x-4)(x-3) & \text { iii) } y=2 x^{2}-5 x-12 \\ \text { d) } y=(3-4 x)(4-x) & \text { iv) } y=3 x^{2}-13 x+12 \\ \text { e) } y=(x+3)(3 x-4) & \text { v) } y=3 x^{2}+5 x-12\end{array} </code></p>
<p>Determine the vertex, the axis of symmetry, the direction the parabola opens, and the number of zeros for each quadratic function. Sketch a graph of each.</p><p><code class='latex inline'> \displaystyle f(x) = 2x^2 + 4x + 7 </code></p>
<p> Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=x^{2}+6 x+3 </code></p>
<ol> <li>Communication The axis of symmetry of the graph of <code class='latex inline'>\displaystyle y=x^{2}-2 x-8 </code> passes through the vertex. Use symmetry to find the <code class='latex inline'>\displaystyle x </code>-coordinate of the vertex. Explain your reasoning.</li> </ol>
<p>Write an equation, in the form <code class='latex inline'>y=ax^2+bx+c</code>, to represent each parabola.</p><p>b)</p><img src="/qimages/1114" />
<p>Determine the maximum or minimum of each function.</p><p> <code class='latex inline'>\displaystyle f(x)=x^{2}+2 x-35 </code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=-4 x^{2}+12 x+7 </code></p>
<p>Find the x-intercepts of the parabola.</p><p><code class='latex inline'>\displaystyle y = x^2 + 2x -3 </code></p>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=10 x^{2}-20 x+12 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=-x^{2}+8 x-12 </code></p>
<p>Graph each quadratic function by hand by determining the zeros, vertex, axis of symmetry, and <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=-x^{2}-2 x+24 </code></p>
<p>Write an equation in the form <code class='latex inline'>y = ax^2 + bx + c</code> to represent each parabola.</p><img src="/qimages/14070" />
<p>The vertex of the parabola <code class='latex inline'>y=3x^2+bx+c</code> is at <code class='latex inline'>(-1,4)</code>. Determine the values of <code class='latex inline'>b</code> and <code class='latex inline'>c</code></p>
<p>Investigate the number of zeros of the function <code class='latex inline'>f(x)=(k + 1)x^2 + 2kx + k - 1</code> for different values of <code class='latex inline'>k</code>. For what values of <code class='latex inline'>k</code> does the function have no zeros? one zero? two zeros?</p>
<p>Graph each function, and then use the graph to locate the zeros.</p><p><code class='latex inline'>\displaystyle f(x)=8 x^{2}+6 x+1 </code></p>
<p>The six graphs represent the six equations <code class='latex inline'> y=x^{2}+4 x, y=x^{2}-4 x </code> <code class='latex inline'> y=-x^{2}+4 x, y=-x^{2}-4 x, y=x^{2}-4 </code> , and <code class='latex inline'> y=-x^{2}+4 . </code> Match each graph with the correct equation.</p><img src="/qimages/64161" />
<p>The six graphs represent the six equations <code class='latex inline'> y=x^{2}+4 x, y=x^{2}-4 x </code> <code class='latex inline'> y=-x^{2}+4 x, y=-x^{2}-4 x, y=x^{2}-4 </code> , and <code class='latex inline'> y=-x^{2}+4 . </code> Match each graph with the correct equation.</p><img src="/qimages/64157" />
<p>Express each function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex without graphing.</p><p><code class='latex inline'>\displaystyle g(x)=3 x^{2}-6 x </code></p>
<ol> <li>The <code class='latex inline'>\displaystyle x </code>-intercepts of a quadratic function are the <code class='latex inline'>\displaystyle x </code>-coordinates of the points where the graph crosses the <code class='latex inline'>\displaystyle x </code>-axis, or where <code class='latex inline'>\displaystyle y=0 </code>. For the function <code class='latex inline'>\displaystyle y=x^{2}-2 x-8 </code>, let <code class='latex inline'>\displaystyle y=0 </code> and solve the resulting quadratic equation by factoring.</li> </ol>
<p>State the maximum or minimum value of <code class='latex inline'> y </code> and the value of <code class='latex inline'> x </code> when it occurs.</p><p><code class='latex inline'>\displaystyle y=-3 x^{2}+18 x-28 </code></p>
<p>Write in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle f(x) = 3x^2 + 12x +19 </code></p>
<p>Determine two points that are the same distance from the axis of symmetry of the quadratic relation <code class='latex inline'>y=4x^2-12x+5</code></p>
<p>Determine the maximum or minimum of each function.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}-9 x-18 </code></p>
<p>State whether you agree or disagree with each statement. Explain why.</p> <ul> <li>All parabolas that open downward have second differences that are positive.</li> </ul>
<ol> <li>Sketch the graphs of the following quadratic functions by factoring to locate the <code class='latex inline'> x </code> -intercepts, and then finding the coordinates of the vertex.</li> </ol> <p><code class='latex inline'>\displaystyle y=x^{2}-4 x-5 </code></p>
<p>Find the value(s) of <code class='latex inline'>b</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p><code class='latex inline'>y=x^2+bx+16</code></p>
<p> Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=x^{2}-2 x+3 </code></p>
<p>Find the value(s) of <code class='latex inline'>b</code> so that each quadratic relation has only one zero. Then, sketch its graph.</p><p><code class='latex inline'>y=-x^2+bx-36</code></p>
<p>For <code class='latex inline'>f(x) = x^2 -4x +1</code>, find</p><p>the coordinates of point <code class='latex inline'>A</code>, where <code class='latex inline'>x = 3</code></p>
<p>Graph each function.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}+4 x+4 </code></p>
<p>Without drawing the graph identify the function that has two zeros.</p><p>A. <code class='latex inline'>n(x) = -x^2 -6x -9</code></p><p>B. <code class='latex inline'>m(x) = 4(x + 1)^2 + 0.5</code></p><p>C. <code class='latex inline'>f(x) = -5(x + 1.3)^2</code></p><p>D. <code class='latex inline'>g(x) = -2(x + 3.6)^2 + 4.1</code></p>
<p>Graph each function.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}-8 x+7 </code></p>
<p>Use the graph of each quadratic relation to determine the roots to each quadratic equation, where <code class='latex inline'>y=0</code>.</p><img src="/qimages/856" />
<p>Determine the zeros and the maximum or minimum value for each function.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}+18 x+16 </code></p>
<p> State whether the graph of each quadratic relation opens upward or downward. Explain how you know.</p><p><strong>a)</strong> <code class='latex inline'> \displaystyle y = x^2 - 1 </code></p><p><strong>b)</strong> <code class='latex inline'> \displaystyle y = -x^2 + 5x </code></p><p><strong>c)</strong> <code class='latex inline'> \displaystyle y = -\frac{1}{2}x^2 + 6x -4 </code></p><p><strong>d)</strong> <code class='latex inline'> \displaystyle y = -9x + \frac{1}{2}x^2 + 6 </code></p>
<p>Write each function in vertex form, and then sketch its graph.</p><p><code class='latex inline'>\displaystyle g(x)=2 x^{2}-2 x+7.5 </code></p>
<p>Sketch the graphs of the following</p><p>quadratic functions by factoring to</p><p>find the <code class='latex inline'>\displaystyle x </code>-intercepts, and then deducing the coordinates of the</p><p>vertex.</p><p><code class='latex inline'>\displaystyle y=x^{2}-6 x-7 </code></p>
<p>Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = x^2 + 12x + 30 </code></p>
<p>Determine the zeros and the maximum or minimum value for each function.</p><p><code class='latex inline'>\displaystyle f(x)=6 x^{2}+7 x-3 </code></p>
<p>Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = -x^2 + 6x - 7 </code></p>
<p>Complete the square to find the vertex.</p><p><code class='latex inline'>\displaystyle y = 3x^2 - 15x -24 </code></p>
<p>Show that the function <code class='latex inline'>\displaystyle y=2 x^{2}-3 x+4 </code> cannot have a <code class='latex inline'>\displaystyle y </code>-value less than <code class='latex inline'>\displaystyle 1.5 </code>.</p>
<p>Determine the maximum or minimum value for each quadratic function.</p><p><code class='latex inline'>\displaystyle g(x)=x^{2}+7 x+10 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=-x^{2}-4 x-12 </code></p>
<p>Write each function in the form <code class='latex inline'> y=a(x-h)^{2}+k </code> . Sketch the graph, showing the coordinates of the vertex, the equation of the axis of symmetry, and the coordinates of two other points on the graph.</p><p><code class='latex inline'>\displaystyle y=x^{2}+10 x+30 </code></p>
<p>Determine the zeros and the maximum or minimum value for each function.</p><p><code class='latex inline'>\displaystyle f(x)=-x^{2}+8 x-7 </code></p>
<p>Write the function in vertex form.</p><p><code class='latex inline'> \displaystyle f(x) = x^2 + 8x +3 </code></p>
<p>Complete the square to find the vertex.</p><p><code class='latex inline'>\displaystyle y = 2x^2 + 12x -14 </code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=-3 x^{2}-18 x+2 </code></p>
<p>Graph each function, and then use the graph to locate the zeros.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}+2 x-8 </code></p>
<p>Express each function in standard form.</p><p>a) <code class='latex inline'>\displaystyle f(x) = -3(x - 2)^2 + 5 </code></p><p>b) <code class='latex inline'>\displaystyle f(x) = 2(x + 4)(x -6) </code></p>
<p>The six graphs represent the six equations <code class='latex inline'> y=x^{2}+4 x, y=x^{2}-4 x </code> <code class='latex inline'> y=-x^{2}+4 x, y=-x^{2}-4 x, y=x^{2}-4 </code> , and <code class='latex inline'> y=-x^{2}+4 . </code> Match each graph with the correct equation.</p><img src="/qimages/64167" />
<p>Use the discriminant to match each function with its graph.</p><img src="/qimages/90208" />
<p>Write each function in vertex form, and then sketch its graph.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}+10 x+12 </code></p>
<p>Write the function in vertex form.</p><p><code class='latex inline'> \displaystyle f(x) = 2x^2 + 12x + 7 </code></p>
<p>Write an equation, in the form <code class='latex inline'>y=ax^2+bx+c</code>, to represent each parabola.</p><img src="/qimages/1112" />
<p>Express each function in factored form. Then determine the zeros, the equation of the axis of symmetry, and the coordinates of the vertex without graphing.</p><p><code class='latex inline'>\displaystyle g(x)=x^{2}-x-6 </code></p>
<p>Without graphing each function, state whether it has a maximum or a minimum. Give the maximum or minimum value of the function.</p><p><code class='latex inline'>\displaystyle y=x^{2}+10 x-5 </code></p>
<p>Two quadratic function have x-intercepts a -1 and 3, and y-intercepts at <code class='latex inline'>-k</code> and <code class='latex inline'>4k</code>, as shown. The quadrilateral formed by joining the four intercepts has an area of 30 <code class='latex inline'>units^2</code>. Determine the value of <code class='latex inline'>k</code>.</p><img src="/qimages/2963" />
<p>Find the value(s] of k so that the parabola has only one x-intercept.</p><p><code class='latex inline'>\displaystyle y =x^2 + kx + 100 </code></p>
<p>Find the x-intercepts and the vertex of each quadratic relation. Then, sketch its graph.</p><p><code class='latex inline'>\displaystyle y = x^2 +8x + 12 </code></p>
<p>Find the vertex of each parabola. Sketch the graph, labelling the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = 5x^2 - 40x + 76 </code></p>
<p>Determine whether each quadratic function intersects the <code class='latex inline'>x</code>—axis at one point, two points, or not at all. Do not draw the graph.</p><p><code class='latex inline'>f(x)=2x^2+3x+5</code></p>
<p>A parabola passes through points <code class='latex inline'>(3,0), (7,0)</code>, and <code class='latex inline'>(9,-24)</code>.</p> <ul> <li>Determine the equation of the axis of symmetry.</li> </ul>
<p>Use two different strategies to determine the equation of the axis of symmetry of the parabola defined by <code class='latex inline'>y=-2x^2+16x-24</code>. Which strategy do you prefer? Explain why.</p>
<p>Determine whether each quadratic function intersects the <code class='latex inline'>x</code>—axis at one point, two points, or not at all. Do not draw the graph.</p><p><code class='latex inline'>f(x)=9x^2-30x+25</code></p>
<p>Find </p> <ul> <li>i. the equation of the axis of symmetry</li> <li>ii. the coordinates of the vertex</li> <li>iii. the y-intercept</li> <li>iv. the zeros</li> </ul> <p>for </p><p><code class='latex inline'> \displaystyle y = x^2 + 2x - 15 </code></p>
<p>Sketch the graph of each function. Show the coordinates of the vertex, the equation of the axis of symmetry, and any intercepts. State the range.</p><p><code class='latex inline'>\displaystyle y=-x^{2}-2 x+3 </code></p>
<p>Locate the <code class='latex inline'>x</code>-intercepts of the graph of each function.</p><p><code class='latex inline'> \displaystyle f(x) = 3x^2 - 7x - 2 </code></p>
<p>Determine the maximum or minimum of each function.</p><p><code class='latex inline'>\displaystyle f(x)=2 x^{2}+7 x+3 </code></p>
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