5. Q5d
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Similar Question 1
<p>Without graphing, determine the number of zeros that each relation has.</p><p><code class='latex inline'>y=5(x+2)(x+2)</code></p>
Similar Question 2
<p><strong>(a)</strong> Sketch the graph of <code class='latex inline'>f(x) = (x - 2)(x + 6)</code></p><p><strong>(b)</strong> Use your graph to sketch the graph of <code class='latex inline'>g(x) = -2(x - 2)(x + 6)</code>.</p><p><strong>(c)</strong> Sketch the graph of <code class='latex inline'>h(x) = 3(x - 2)(x + 6)</code>.</p>
Similar Question 3
<p>Given the quadratic function <code class='latex inline'>f(x) = 3x^2 -6x + 15</code>, identify the coordinates of the vertex.</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>The sum of two whole numbers is 10 . Their product can be modelled by the function <code class='latex inline'>\displaystyle P(x)=x(10-x) </code>.</p><p>a) What does <code class='latex inline'>\displaystyle x </code> represent? What does <code class='latex inline'>\displaystyle (10-x) </code> represent? What does <code class='latex inline'>\displaystyle P(x) </code> represent?</p><p>b) What is the domain of this function?</p><p>c) Evaluate the function for all valid values of the domain. Show the results in a table of values. <code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|l|l|l|l|l|l|l|} \hline \boldsymbol{x} & 0 & & & & & & & & & & \\ \hline \boldsymbol{P}(\boldsymbol{x}) & 0 & & & & & & & & & & \\ \hline \end{array} </code> d) What two numbers do you estimate give the largest product? What is the largest product? Explain.</p>
<p>Determine an equation in the form <code class='latex inline'> y = a(x-r)(x-s)</code> to represent each of the following parabolas. </p><img src="/qimages/22264" />
<p>Sketch the graph of each function. State the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=-3(x-1)(x+3) </code></p>
<p>Sketch graphs of all three relations on the same set of axes. Label the <em>x</em>-intercepts, vertex, and axis of symmetry for each parabola. Then, describe the similarities and differences between the graphs. </p><p>a) <code class='latex inline'> y = (x-3)(x+1)</code></p><p>b) <code class='latex inline'> y = 2(x-3)(x+1)</code></p><p>c) <code class='latex inline'> y = -2(x-3)(x+1)</code></p>
<p>Complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|c|l|l|l|} \hline \text{Zeros} & \text{Axis of Symmetry} & \text{Maximum or Minimum Value} & \text{Vertex} & \text{Function in Factored Form} & \text{Function in Standard Form} \\ \hline -7 \text{ and } -2 & -2 & & & \\ \hline \end{array} </code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = -0.1(x-2)(x+4)</code></p>
<p>Sometimes the equation <code class='latex inline'>y = a(x -r)(x -s)</code> cannot be used to determine the equation of a parabola from its graph. </p><p>Explain when this is not possible, and draw graphs to illustrate.</p>
<ol> <li>Write an equation in standard form for each quadratic function.</li> </ol> <img src="/qimages/18075" />
<p>Sketch a graph of each relation. Label the x-intercepts and the vertex.</p><p><code class='latex inline'>\displaystyle y = (x-6)(x + 2) </code></p>
<p>Complete the following for each quadratic relation below.</p> <ul> <li><strong>i)</strong> Determine the zeros</li> <li><strong>ii)</strong> Explain how the zeros are related to the facts in the quadratic expression.</li> <li><strong>iii)</strong> Determine the y-intercept.</li> <li><strong>iv)</strong> Determine the equation of the xis of symmetry.</li> <li><strong>v)</strong> Determine the coordinates of the vertex.</li> <li><strong>vi)</strong> is the graph a parabola? How can you tell?</li> <li><strong>vii)</strong> Sketch the graph.</li> </ul> <p><code class='latex inline'>y = 2(x - 1)(x + 2)</code></p>
<ul> <li>i) determine the coordinates of two points on the graph that are the same distance from the axis of symmetry</li> <li>ii) determine the equation of the axis of symmetry </li> <li>iii) determine the coordinates of the vertex</li> <li>iv) write the relation in vertex form</li> </ul> <p> <code class='latex inline'>y=(x-1)(x+7)</code></p>
<p> Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. </p><p><code class='latex inline'>y = (x -3)(x + 3)</code> </p>
<p>Sketch a graph of each relation. Label the x-intercepts and the vertex.</p><p><code class='latex inline'>\displaystyle y = -4(x-1)(x - 9) </code></p>
<p>Graph each function, and complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|l|l|} \hline Factored Form & Standard Form & Axis of Symmetry & Zeros & y -intercept & Vertex & Maximum or Minimum Value \\ \hline f(x)=(x-4)(x+2) & & & & & \\ \hline \end{array} </code></p>
<p>Write the function <code class='latex inline'> \displaystyle f(x) = (x - 7)(x +5) </code> in vertex form.</p>
<p>Use a graphing calculator to graph each relation. Describe and justify how the shape of the graph relates to the number of factors. </p><p>a) <code class='latex inline'> y = 2(x+1)</code></p><p>b) <code class='latex inline'> y = 2(x+1)(x+2)</code></p><p>c) <code class='latex inline'> y = 2(x+1)(x+2)(x+3)</code></p><p>d) <code class='latex inline'> y = 2(x+1)(x+2)(x+3)(x+4) </code></p>
<p>Complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|c|l|l|l|} \hline \text{Zeros} & \text{Axis of Symmetry} & \text{Maximum or Minimum Value} & \text{Vertex} & \text{Function in Factored Form} & \text{Function in Standard Form} \\ \hline -1 \text{ and } 9 & & 5 & & & \\ \hline \end{array} </code></p>
<ol> <li>Determine an equation, in factored form, for a family of quadratic functions with the given roots. Draw a sketch to illustrate each family.</li> </ol> <p> <code class='latex inline'>\displaystyle x=-3 </code> and <code class='latex inline'>\displaystyle x=-6 </code></p>
<p>For each quadratic function, 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+3)(x-2) </code></p>
<p>Determine the equation of each parabola.</p><img src="/qimages/164691" />
<p>For the graph, write the equation in both factored and standard forms.</p><img src="/qimages/22322" />
<p>If <code class='latex inline'>f(x) = (x - 2)(x + 5)</code>, determine the x-intercepts for the function <code class='latex inline'> y=f(-(x + 2))</code>.</p>
<p>Determine the equation of the parabola with <code class='latex inline'>x</code>-intercepts</p><p><code class='latex inline'>-4</code> and <code class='latex inline'>3</code>, and that passes through <code class='latex inline'>(2, 7)</code></p>
<p>For each quadratic function, 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)=(5-x)(5+x) </code></p>
<p>Without graphing, determine the number of zeros that each relation has.</p><p><code class='latex inline'>y=5(x+2)(x+2)</code></p>
<p>Sketch the graph of each relation.</p><p><strong>a)</strong> <code class='latex inline'>y = (x -3)(x + 3)</code> </p><p><strong>b)</strong> <code class='latex inline'>y = (x + 2)(x + 2)</code> </p><p><strong>c)</strong> <code class='latex inline'>y = (x - 2)(x - 2)</code></p><p><strong>d)</strong> <code class='latex inline'> y = -(x -2)(x + 2)</code></p><p><strong>e)</strong> <code class='latex inline'> y = 2(x + 3)^2</code> </p><p><strong>f)</strong> <code class='latex inline'>y = -4(x -4)^2</code> </p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = 3(x-2)(x+1)</code></p>
<p>Write each function in standard form.</p><p><code class='latex inline'>\displaystyle f(x)=-(2 x+3)(4 x-5) </code></p>
<ol> <li>Write the equation for a quadratic</li> </ol> <p>function that has the given <code class='latex inline'>\displaystyle x </code>-intercepts and that passes through the given point. Express each equation in factored form.</p><p>a) <code class='latex inline'>\displaystyle x </code>-intercepts: <code class='latex inline'>\displaystyle -3 </code> and 4 , point: <code class='latex inline'>\displaystyle (1,-24) </code></p>
<p>Sketch the graph of each function. State the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=(x+2)(x-4) </code></p>
<p>Determine the zeros, equation of the axis of symmetry, and vertex of Q each parabola. Then determine an equation for each quadratic relation. </p><img src="/qimages/1508" />
<p>Sketch the graph of each function. State the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=(x+1)(x+3) </code></p>
<p>Write each function in standard form.</p><p><code class='latex inline'>\displaystyle f(x)=(x+7)(2 x+3) </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)=(3 x-1)(2 x-5) </code></p>
<p>A student claims that the discriminant of a quadratic relation will never be negative if the relation can be written in the form <code class='latex inline'>y=a(x-4)(x-s)</code>. Do you agree or disagree? Explain.</p>
<p>Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. Then sketch its graph.</p><p><code class='latex inline'>\displaystyle y = 2(x-1)(x+3) </code></p>
<p>Write the standard form of the quadratic equation for each case.</p><p><code class='latex inline'>\displaystyle \begin{array}{llc} & x \text {-intercepts } & y \text {-intercept } \\ \text { a) } & -3 \text { and } 4 & 24 \end{array} </code></p>
<p>Express the quadratic relation <code class='latex inline'>y=2(x-4)(x+10)</code> in both standard form and vertex form.</p>
<p>Determine the zeros, the coordinates of the vertex, and the <code class='latex inline'>\displaystyle y </code>-intercept for each function.</p><img src="/qimages/164719" />
<ol> <li>Write the equation for a quadratic</li> </ol> <p>function that has the given <code class='latex inline'>\displaystyle x </code>-intercepts and that passes through the given point. Express each equation in factored form.</p><p>c) <code class='latex inline'>\displaystyle x </code>-intercepts: 0 and <code class='latex inline'>\displaystyle \frac{2}{3} </code>, point: <code class='latex inline'>\displaystyle (2,-32) </code></p>
<p>Express each quadratic function in standard form. Determine the <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=(3 x-4)(2 x+5) </code></p>
<ol> <li>Write the equation for a quadratic</li> </ol> <p>function that has the given <code class='latex inline'>\displaystyle x </code>-intercepts and that passes through the given point. Express each equation in factored form.</p><p>b) <code class='latex inline'>\displaystyle x </code>-intercepts: <code class='latex inline'>\displaystyle -2 </code> and 5, point: <code class='latex inline'>\displaystyle (-1,3) </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-1)(x-4) </code></p>
<p>Consider the quadratic function <code class='latex inline'>f(x) = 4(x - 2)(x + 6)</code>.</p><p>Graph the function.</p>
<p>Describe the transformations that were applied to <code class='latex inline'>y = x^2</code> to obtain each of the following functions.</p><p><code class='latex inline'>y =(x + \frac{3}{8})(x + \frac{3}{7}) </code></p>
<ul> <li>Express the equation <code class='latex inline'>y = 2(x + 3)(x - 1)</code> in standard form.</li> </ul>
<p>Write each quadratic relation in vertex form using an appropriate strategy.</p><p><code class='latex inline'>\displaystyle y = -2(x+ 3)(x -7) </code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = (x+2)(x-4)</code></p>
<p>Determine the equation of each parabola.</p><img src="/qimages/164690" />
<p>Determine the zeros, equation of the axis of symmetry, and vertex of <code class='latex inline'>Q</code> each parabola. Then determine an equation for each quadratic relation. </p><img src="/qimages/1506" />
<p>For each quadratic function, 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-10)(2-x) </code></p>
<p>A parabola has equation <code class='latex inline'>y = (x +4)(x-2)</code>.</p><p>a) Find the x-intercepts of <code class='latex inline'>y= (x+4)(x-2)</code>.</p><p>b) Expand and simplify the equation.</p><p>e) Graph the result from part b). Verify that the x-intercepts are the same.</p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = -(x+3)(x-5)</code></p>
<p>A glider is launched from a tower on a hilltop. The height, in metres, is negative whenever the glider is below the height of the hilltop. The equation representing the flight is <code class='latex inline'>\displaystyle h(t)=\frac{1}{4}(t-3)(t-12) </code>, where time, <code class='latex inline'>\displaystyle t </code>, is measured in seconds.</p><img src="/qimages/163379" /><p>Time <code class='latex inline'>\displaystyle (s) </code> a) What does <code class='latex inline'>\displaystyle h(0) </code> represent?</p><p>b) What does <code class='latex inline'>\displaystyle h(3) </code> represent?</p><p>c) When is the glider at its lowest point? What is the vertical distance between the top of the tower and the glider at this time?</p>
<p>Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. Then sketch its graph.</p><p><code class='latex inline'>\displaystyle y = (x-5)(x+ 5) </code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = (x + \dfrac{1}{4})(x-\dfrac{1}{2})</code></p>
<p>Without solving, determine the number of real roots it has.</p><p><code class='latex inline'>y =3(x-4)(x-4)</code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = \dfrac{1}{2} (x-3)(x+5)</code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = -\dfrac{1}{3}(x+0.2)(x-0.4)</code></p>
<p> A quadratic relation has an equation of the form <code class='latex inline'>y = a(x - r)(x -s)</code> The graph of the relation has zeros at (2, 0) and (-6, 0) and passes through the point (3, 5). Determine the value of <code class='latex inline'>a</code>.</p>
<p>A quadratic relation has an equation of the form <code class='latex inline'>y = a(x -r)(x - s)</code>. Determine the value of <code class='latex inline'>a</code> when</p><p>the parabola has x-intercepts at <code class='latex inline'>(5, 0)</code> and <code class='latex inline'>(-3, 0)</code> and a maximum value of <code class='latex inline'>6</code>.</p>
<p>A quadratic relation has an equation of the form <code class='latex inline'>y = a(x -r)(x - s)</code>. Determine the value of <code class='latex inline'>a</code> when</p><p>the parabola has its vertex at <code class='latex inline'>(5, 0)</code> and a y-intercept at <code class='latex inline'>(0, -10)</code>.</p>
<p> Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. </p><p><code class='latex inline'>y = (x - 2)(x - 2)</code></p>
<ol> <li>Determine an equation, in factored form, for a family of quadratic functions with the given roots. Draw a sketch to illustrate each family.</li> </ol> <p> <code class='latex inline'>\displaystyle x=1 </code> and <code class='latex inline'>\displaystyle x=-4 </code></p>
<p>Determine the zeros, equation of the axis of symmetry, and vertex of Q each parabola. Then determine an equation for each quadratic relation. </p><img src="/qimages/1507" />
<p>Without graphing, match each quadratic relation in factored form in column 1 with the equivalent quartic relation in standard form in column 2. Explain your reasoning.</p><p><code class='latex inline'> \begin{array}{cccccccc} && Column 1 &&Column 2\\ &(a) & y = (2x - 3)(x + 4) &i) & y = 12x^2 - 5x -3 \\ &(b) & y = (3x + 1)(4x - 3) & ii) &y = -2x^2 - 5x + 12 \\ &(c) & y = (3- 2x)(4 + x) &iii) & y = 2x^2 + 11x -12 \\ &(d) & y = (3 -4x)(1 + 3x) & iv) & y = 2x^2 + 5x -12 \\ &&&v)& y = -12x^2 + 5x + 3\\ &&&vi)& y = 12x^2 5x - 3\\ \end{array} </code></p>
<ol> <li>Write an equation in standard form for each quadratic function.</li> </ol> <img src="/qimages/18074" />
<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=2x(x-4)</code></p>
<p>Determine the equation of the parabola with <code class='latex inline'>x</code>-intercepts</p><p><code class='latex inline'>\sqrt{7}</code> and <code class='latex inline'>-\sqrt{7}</code>, that passes through (-5, 3)</p>
<p>A parabola has equation <code class='latex inline'> y = -(x-4)^2</code>. </p><p>a) State the direction of opening. </p><p>b) Write the coordinates of the vertex of the parabola. </p><p>c) Write the <em>x</em>-intercept(s) of the parabola. </p><p>d) Rewrite the equation in the form <code class='latex inline'> y = a(x-r)(x-s)</code>. </p>
<p>The parabola has equation <code class='latex inline'> y = (x+3)^2</code>. </p><p>a) State the direction of opening. </p><p>b) Write the coordinates of the vertex of the parabola. </p><p>c) Write the <em>x</em>-intercept(s) of the parabola. </p><p>d) Rewrite the equation in the form <code class='latex inline'> y = a(x-r)(x-s)</code>.</p>
<p>Determine an equation in the form <code class='latex inline'> y = a(x-r)(x-s)</code> to represent each of the following parabola. </p><img src="/qimages/22265" />
<p>Sketch the graph of <code class='latex inline'>y= a(x - 2)(x + 3)</code>if the value of <code class='latex inline'>a</code> changed to 2, 1, 0, -1, -2, and -3. </p>
<p>Graph each function, and complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|l|l|} \hline Factored Form & Standard Form & Axis of Symmetry & Zeros & y -intercept & Vertex & Maximum or Minimum Value \\ \hline p(x)=(3-x)(x+1) & & & & & & \\ \hline \end{array} </code></p>
<p>Sketch graphs of all three relations on the same set of axes. Label the <em>x</em>-intercepts, vertex, and axis of symmetry for each parabola. Then, describe the similarities and differences between the graphs. </p><p>a) <code class='latex inline'> y = (x+4)(x-2)</code></p><p>b) <code class='latex inline'> y = \dfrac{1}{2}(x+4)(x-2)</code></p><p>c) <code class='latex inline'> y = \dfrac{1}{4}(x+4)(x-2)</code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = 2x(x-4)</code></p>
<p>Graph </p><p><code class='latex inline'>\displaystyle f(x) = 2(x + 4)(x -6) </code></p>
<p>Sketch the graph of each function. State the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y=(2 x+1)(x-2) </code></p>
<p>What characteristics will two parabola in the family <code class='latex inline'>f(x) = a(x - 3)(x + 4)</code> share?</p>
<ol> <li>Determine an equation, in factored form, for a family of quadratic functions with the given roots. Draw a sketch to illustrate each family.</li> </ol> <p> <code class='latex inline'>\displaystyle x=5 </code> and <code class='latex inline'>\displaystyle x=-2 </code></p>
<p>Given the quadratic function <code class='latex inline'>f(x) = 3x^2 -6x + 15</code>, identify the coordinates of the vertex.</p>
<p>Determine the maximum or minimum value for each quadratic function.</p><p><code class='latex inline'>\displaystyle f(x)=(7-x)(x+2) </code></p>
<p>Match each quartic relation with the correct parabola. </p><p><code class='latex inline'>\begin{array}{cccccccc} &(a) &y = (x - 2)(x + 3) & (d) & y = (3 -x)(x + 2) \\ &(b) &y = (x - 3)(x + 2) & (e) & y = (3 + x)(2 - x) \\ &(c) &y = (x + 2)(x + 3) & (f) & y = ( x - 2)(x - 3) \\ \end{array} </code></p><img src="/qimages/1505" />
<p>For each quadratic function, 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+5)(9-2 x) </code></p>
<p>For each quadratic function, 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-8)(x+4) </code></p>
<p>Complete the following for each quadratic relation below.</p> <ul> <li><strong>i)</strong> Determine the zeros</li> <li><strong>ii)</strong> Explain how the zeros are related to the facts in the quadratic expression.</li> <li><strong>iii)</strong> Determine the y-intercept.</li> <li><strong>iv)</strong> Determine the equation of the xis of symmetry.</li> <li><strong>v)</strong> Determine the coordinates of the vertex.</li> <li><strong>vi)</strong> is the graph a parabola? How can you tell?</li> <li><strong>vii)</strong> Sketch the graph.</li> </ul> <p><code class='latex inline'>y = -2x(x + 3)</code></p>
<p>Sketch each graph. Label the intercepts and the vertex using their coordinates.</p><p><code class='latex inline'>\displaystyle y = -(x-6)(x + 4) </code></p>
<p>Find the zeros of each function.</p><p><code class='latex inline'>\displaystyle y = x(x-6) </code></p>
<p><strong>(a)</strong> Sketch the graph of <code class='latex inline'>f(x) = (x - 2)(x + 6)</code></p><p><strong>(b)</strong> Use your graph to sketch the graph of <code class='latex inline'>g(x) = -2(x - 2)(x + 6)</code>.</p><p><strong>(c)</strong> Sketch the graph of <code class='latex inline'>h(x) = 3(x - 2)(x + 6)</code>.</p>
<p>Sketch a graph of each quadratic. Label the x-intercepts and the vertex.</p><p><code class='latex inline'>\displaystyle y = 2(x - 3)(x +1) </code></p>
<p>Graph each function, and complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|l|l|l|l|l|} \hline Factored Form & Standard Form & Axis of Symmetry & Zeros & y -intercept & Vertex & Maximum or Minimum Value \\ \hline R(x)=(40-x)(10+x) & R(x)=-x^{2}+30 x+400 & & & & & \\ \hline \end{array} </code></p>
<p>Write each function in standard form.</p><p><code class='latex inline'>\displaystyle g(x)=-(5-3 x)(-2 x+1) </code></p>
<p>Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. Then sketch its graph.</p><p><code class='latex inline'>\displaystyle y = -(x-6)(x-2) </code></p>
<p>Factor the quadratic relation <code class='latex inline'>y=2x^2-3x</code> to find the <code class='latex inline'>x</code>-intercepts.</p>
<p>Complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|c|l|l|l|} \hline \text{Zeros} & \text{Axis of Symmetry} & \text{Maximum or Minimum Value} & \text{Vertex} & \text{Function in Factored Form} & \text{Function in Standard Form} \\ \hline -8 \text{ and } 0 & & -5 & & & \\ \hline \end{array} </code></p>
<p>Consider the quadratic function <code class='latex inline'>f(x) = 4(x - 2)(x + 6)</code>.</p><p>Determine the coordinates of the vertex.</p>
<p>For each graph, write the equation in both factored and standard forms.</p><img src="/qimages/163706" />
<p>Determine the equation of the parabola with <code class='latex inline'>x</code>-intercepts</p><p><code class='latex inline'>0</code> and <code class='latex inline'>8</code>, and that passes through <code class='latex inline'>(-3, -6)</code></p>
<p>Write the equation of the graph in vertex form.</p><img src="/qimages/5260" />
<p>A quadratic relation has an equation of the form <code class='latex inline'>y = a(x -r)(x - s)</code>. Determine the value of <code class='latex inline'>a</code> when</p><p>the parabola has zeros at <code class='latex inline'>(4, 0)</code> and <code class='latex inline'>(2, 0)</code> and a <code class='latex inline'>y</code>-intercept at <code class='latex inline'>(0, 1)</code>.</p>
<p>Determine the number of zeros. Do not use the same method for all four parts.</p><p><code class='latex inline'> \displaystyle f(x) = 5(x - 3)(x + 4) </code></p>
<p>The points <code class='latex inline'>(-9, 0)</code> and <code class='latex inline'>(19, 0)</code> lie on a parabola.</p><p>a) Determine an equation for its axis of symmetry.</p><p>b) The y—coordinate of the vertex is -28. Determine an equation for the parabola in factored form.</p><p>c) Write your equation for part b) in standard form.</p>
<p>Sketch the graph of <code class='latex inline'>y= a(x - 2)(x + 3)</code> when <code class='latex inline'>a= 3</code></p>
<p>Sketch a graph of each quadratic. Label the x-intercepts and the vertex.</p><p><code class='latex inline'>\displaystyle y = -(x + 5)(x -7) </code></p>
<p>Find the zeros of each function.</p><p><code class='latex inline'>\displaystyle y = (x + 4)(x - 5) </code></p>
<p>Determine the zeros, the coordinates of the vertex, and the <code class='latex inline'>\displaystyle y </code>-intercept for each function.</p><img src="/qimages/164718" />
<p>Determine the maximum or minimum value for each.</p><p>(c) <code class='latex inline'> \displaystyle f(x) = -2x(x - 4) </code></p><p>(d) <code class='latex inline'> \displaystyle g(x) = 2x^2 - 7 </code></p>
<p>Complete the following for each quadratic relation below.</p> <ul> <li><strong>i)</strong> Determine the zeros</li> <li><strong>ii)</strong> Explain how the zeros are related to the facts in the quadratic expression.</li> <li><strong>iii)</strong> Determine the y-intercept.</li> <li><strong>iv)</strong> Determine the equation of the xis of symmetry.</li> <li><strong>v)</strong> Determine the coordinates of the vertex.</li> <li><strong>vi)</strong> is the graph a parabola? How can you tell?</li> <li><strong>vii)</strong> Sketch the graph.</li> </ul> <p><code class='latex inline'>y = (x - 3)(x + 1)</code></p>
<p>Express each quadratic function in standard form. Determine the <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=2(x-4)(3 x+2) </code></p>
<p>Complete the table.</p><p><code class='latex inline'>\displaystyle \begin{array}{|l|l|c|l|l|l|} \hline \text{Zeros} & \text{Axis of Symmetry} & \text{Maximum or Minimum Value} & \text{Vertex} & \text{Function in Factored Form} & \text{Function in Standard Form} \\ \hline 2 \text{ and } 8 & 6 & & & \\ \hline \end{array} </code></p>
<p>Determine the maximum or minimum value of </p><p><code class='latex inline'>\displaystyle f(x) = 2(x-4)(x+ 6) </code></p>
<p>Without graphing, determine the number of x-intercepts that the relation has.</p><p><code class='latex inline'>\displaystyle y = (x-4)(2x + 9) </code></p>
<p>Write the standard form of the quadratic equation for each case.</p><p><code class='latex inline'>\displaystyle \begin{array}{llc} & x \text {-intercepts } & y \text {-intercept } \\ & -2 \text { and }-5 & 10 \end{array} </code></p>
<p>Without graphing, determine the number of zeros that each relation has.</p><p> <code class='latex inline'>y=x(x-7)</code></p>
<p>A quadratic relation has an equation of the form <code class='latex inline'>y = a(x -r)(x - s)</code>. Determine the value of <code class='latex inline'>a</code> when</p><p>the parabola has zeros at <code class='latex inline'>(5, 0)</code> and <code class='latex inline'>(0, 0)</code> and a minimum value of <code class='latex inline'>-10</code>.</p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = -2(x+2)(x-3)</code></p>
<p>A parabola passes through the points <code class='latex inline'>(-4,10), (-3,0), (-2 -6), (-1, -8), (0, -6), (l, 0),</code> and <code class='latex inline'>(2, l0)</code>.</p><p>Determine an equation for the parabola in factored form.</p>
<ol> <li>Write an equation in standard form for each quadratic function.</li> </ol> <img src="/qimages/18076" />
<p> Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. </p><p><code class='latex inline'> y = -(x -2)(x + 2)</code></p>
<p>When the equation of a quadratic function is in factored form, which feature is most easily determined?</p><p>a) y-intercept</p><p>b) x-intercept</p><p>c) vetex</p><p>d) maximum value</p>
<p>State the direction of opening and the zeros of the function, <code class='latex inline'>f(x) = 4(x - 2)(x + 6)</code>.</p>
<p>Express each quadratic function in standard form. Determine the <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=3 x(x-4) </code></p>
<p>Write the standard form of the quadratic equation for each case.</p><p><code class='latex inline'>\displaystyle \begin{array}{llc} & x \text {-intercepts } & y \text {-intercept } \\ & 5 \text { and }-7 & -105\end{array} </code></p>
<p> Determine the y-intercept, zeros, equation of the axis of symmetry, and vertex of each quadratic relation. </p><p><code class='latex inline'>y = (x + 2)(x + 2)</code> </p>
<p>Write each function in standard form.</p><p><code class='latex inline'>\displaystyle g(x)=(6-x)(3 x+2) </code></p>
<p>For each quadratic function, state the maximum or minimum value of where it will occur.</p><p><code class='latex inline'>f(x) = 4x(x + 6)</code></p>
<p>Write the equation of the graph in vertex form.</p><img src="/qimages/5259" />
<p>Determine the maximum or minimum value for each quadratic function.</p><p><code class='latex inline'>\displaystyle f(x)=(x+5)(x-9) </code></p>
<p>Express each quadratic function in standard form. Determine the <code class='latex inline'>\displaystyle y </code>-intercept.</p><p><code class='latex inline'>\displaystyle f(x)=(x-5)(x+7) </code></p>
<p><strong>a)</strong> Sketch the graph of <code class='latex inline'>y = (x -2)(x -s)</code> when <code class='latex inline'>s = 3</code></p><p><strong>b)</strong> Describe how your graph for part (a) would change if the value of s changed to <code class='latex inline'>2, 1, 0, 1, -2</code>, and <code class='latex inline'>-3</code>.</p>
<p>Write the standard form of the quadratic equation for each case.</p><p><code class='latex inline'>\displaystyle \begin{array}{llc} & x \text {-intercepts } & y \text {-intercept } \\ & \text { 4 and } 2 & -24\end{array} </code></p>
<p>A quadratic relation has an equation of the form <code class='latex inline'>y = a(x -r)(x - s)</code>. Determine the value of <code class='latex inline'>a</code> when</p><p>the parabola has x-intercepts at <code class='latex inline'>(4, 0)</code> and <code class='latex inline'>(-2, 0)</code> and a y-intercept at <code class='latex inline'>(0, -1)</code>.</p>
<p>The coordinates of the vertex for the graph of <code class='latex inline'>y =(x + 2)(x -3)</code> are</p><p>A. <code class='latex inline'>(-2, 3)</code></p><p>B. <code class='latex inline'>( - \frac{1}{2}, -\frac{21}{4})</code></p><p>C. <code class='latex inline'>(2, 3)</code></p><p>D. <code class='latex inline'>(\frac{1}{2}, - \frac{25}{4})</code></p>
<p>Find the zeros of each function. Then graph the function.</p><p><code class='latex inline'>\displaystyle y=(x-1)(x+2) </code></p>
<p>Sketch each graph. Label the intercepts and the vertex using their coordinates.</p><p><code class='latex inline'>\displaystyle y = (x-6)(x + 2) </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=-0.5x(x-8)</code></p>
<p>Sketch the parabola. Label the <em>x</em>-intercepts and vertex. </p><p><code class='latex inline'> y = (x+2.5)(x-2.5)</code></p>
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