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Similar Question 1
<p>Graph the parabola by completing the square. Label the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = x^2 + 6x + 4 </code></p>
Similar Question 2
<p> Complete the square to express each quadratic relation in the form <code class='latex inline'>y = a(x-h)^2 + k</code>. Then, give the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y = x^2 + 4x + 1 </code></p>
Similar Question 3
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = -\frac{1}{2}x^2 - x + \frac{3}{2}</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 the relation in vertex form by completing the square.</p><p><code class='latex inline'>y=x^2-12x-3</code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. Use algebra tiles or a diagram to support your solution.</p><p><code class='latex inline'>\displaystyle y = x^2 + 4x +6 </code></p>
<p>Determine the coordinates of the vertex of each relation.</p><p><code class='latex inline'>\displaystyle y = 2x^2 -24x + 72 </code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>f(x) = x^2 + 13x +2</code></p>
<p>Find the vertex of each quadratic relation by completing the square.</p><p><code class='latex inline'>y=x^2+6x+2</code></p>
<p>Use algebra tiles to rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2+8x+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'>y=-x^2-6x+3</code></p>
<p>Complete the square to express each relation in vertex form. Then describe the transformations that must be applied to the graph of <code class='latex inline'>y=x^2</code> to graph the relation.</p><p> <code class='latex inline'>y=-3x^2+12x-6</code></p>
<p>Find the vertex of each quadratic relation by completing the square.</p><p> <code class='latex inline'>y=x^2-8x+13</code></p>
<p> Complete the square to express each quadratic relation in the form <code class='latex inline'>y = a(x-h)^2 + k</code>. Then, give the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y = x^2 + 4x + 1 </code></p>
<p>Determine whether the vertex of each parabola lies above, below, or on the x-axis. Explain how you know,</p><p><code class='latex inline'>h=2t^2-4t+1.5</code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>y = x^2 -11x -4</code></p>
<p>Determine whether the vertex of each parabola lies above, below, or on the x-axis. Explain how you know,</p><p><code class='latex inline'>h=0.5t^2-4t+7.75</code></p>
<p>Complete the square to write each quadratic relation in vertex form.</p><p><code class='latex inline'>\displaystyle y = 0.2x^2-0.4x + 1 </code></p>
<p>Determine the maximum or minimum value of each relation by completing the square.</p><p><code class='latex inline'>y=-4.9x^2-19.6x+0.5</code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=3x^2-12x-5</code></p>
<p>Determine the maximum or minimum value of each relation by completing the square.</p><p><code class='latex inline'>y=-12x^2+96x+6</code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = -x^2 + 12x - 5</code></p>
<p>Rewrite each equation in vertex form.</p><p><code class='latex inline'>\displaystyle y=2 x^{2}-6 x-1 </code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>\displaystyle y=x^{2}+4 x </code></p>
<p>Complete the square to write each quadratic relation in vertex form.</p><p><code class='latex inline'>\displaystyle y = -3x^2 + 12x -2 </code></p>
<p>Copy and replace each symbol to complete the square.</p><p><code class='latex inline'>\displaystyle y=x^{2}+12 x+5 </code></p><p><code class='latex inline'>\displaystyle y=x^{2}+12 x+\square-\square+5 </code></p><p><code class='latex inline'>\displaystyle y=\left(x^{2}+12 x+\square\right)-\square+5 </code></p><p><code class='latex inline'>\displaystyle y=(x+ \diamondsuit)^{2}-\bigcirc </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'>y=x^2-16x+60</code></p>
<p>Determine the coordinates of the vertex of each relation.</p><p><code class='latex inline'>\displaystyle y = x^2 + 10x + 25 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p> <code class='latex inline'>y=x^2+2x+7</code></p>
<p>Write the relation in vertex form by completing the square.</p><p><code class='latex inline'>y=x^2+8x+6</code></p>
<p>Complete the square to express each relation in vertex form. Then describe the transformations that must be applied to the graph of <code class='latex inline'>y=x^2</code> to graph the relation.</p><p><code class='latex inline'>y=x^2-8x+4</code></p>
<p> Find the vertex of the following parabolas and state which parabola(with its vertex at the origin) it is congruent to. </p><p><code class='latex inline'>\displaystyle y = -x^2 + 10x + 14 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=2x^2+16x+3</code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = \frac{2}{3}x^2 + \frac{16}{3}x + \frac{25}{3}</code></p>
<p>Determine the coordinates of the vertex of each relation.</p><p><code class='latex inline'>\displaystyle y = 2x^2-7x -4 </code></p>
<ol> <li>Complete the square to determine the coordinates of the vertex. State if the</li> </ol> <p>vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=-2 x^{2}+12 x+7 </code></p>
<p>Determine whether the vertex of each parabola lies above, below, or on the x-axis. Explain how you know,</p><p><code class='latex inline'>h=0.5t^2-2t+0.5</code></p>
<p>Find the vertex of each quadratic relation by completing the square.</p><p> <code class='latex inline'>y=x^2+12x+30</code></p>
<p>Write each relation in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle y = -3x^2 -18x - 17 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. Use algebra tiles or a diagram to support your solution.</p><p><code class='latex inline'>\displaystyle y = x^2 + 2x +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'>y=x^2+8x+10</code></p>
<p>Complete the square to state the coordinates of the vertex of each relation.</p><p><code class='latex inline'>y=2x^2+8x</code></p>
<p>Rewrite each equation in vertex form. Then find the vertex of the graph.</p><p><code class='latex inline'>\displaystyle y=\frac{1}{2} x^{2}-5 x+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'>y=x^2+10x+20</code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y = x^2-8x-2</code></p>
<p>Express each equation in factored form and vertex form.</p><p><code class='latex inline'>y = 2x^2 -x - 6</code></p>
<p>Write each relation in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle y = x^2 -4x + 5 </code></p>
<p>Graph the parabola by completing the square. Label the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = 3x^2 + 24x + 10 </code></p>
<p>Determine the maximum or minimum value of each relation by completing the square.</p><p><code class='latex inline'>y=8x^2-96x+15</code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>\displaystyle g(x)=x^{2}-3 x+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'>y=-x^2+4x-2</code></p>
<p>Complete the square to express each relation in vertex form. Then graph the relation.</p><p><code class='latex inline'>y=x^2+10x+20</code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2-2x-8</code></p>
<p>Use algebra tiles to rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2+6x+3</code></p>
<p>Complete the square to express each relation in vertex form. Then describe the transformations that must be applied to the graph of <code class='latex inline'>y=x^2</code> to graph the relation.</p><p><code class='latex inline'>y=2x^2-x+3</code></p>
<p>Complete the square to state the coordinates of the vertex of each relation.</p><p><code class='latex inline'>y=-5x^2-20x+6</code></p>
<ol> <li>Complete the square to determine the coordinates of the vertex. State if the</li> </ol> <p>vertex is a minimum or a maximum.</p><p> <code class='latex inline'>\displaystyle f(x)=x^{2}+4 x+1 </code></p>
<p>Write each relation in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle y = x^2 + 6x -3 </code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>g(x) = x^2 - 3x + 1</code></p>
<p>Determine the coordinates of the vertex of each relation.</p><p><code class='latex inline'>\displaystyle y = -5x^2 + 500 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2+6x-1</code></p>
<p>Use algebra tiles to rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2+4x+7</code></p>
<p>Complete the square to express each relation in vertex form. Then describe the transformations that must be applied to the graph of <code class='latex inline'>y=x^2</code> to graph the relation.</p><p><code class='latex inline'>y=x^2+12x+36</code></p>
<p>Find the <code class='latex inline'>x</code>-intercepts, the vertex, and the equation of the axis of symmetry of each quadratic relation. Then, sketch the parabola.</p><p> <code class='latex inline'>y=-x^2-3x-3</code></p>
<p>How does changing the value of the constant term in the relation <code class='latex inline'>y=2x^2-4x+5</code> affect the coordinates of the vertex?</p>
<p>Explain how to determine the vertex of <code class='latex inline'>y=x^2-2x-35</code> using three different strategies. Which strategy do you prefer? Explain your choice.</p>
<p>Rewrite each relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. Use algebra tiles or a diagram to support your solution.</p><p><code class='latex inline'>\displaystyle y = x^2 + 6x - 3 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2-12x+8</code></p>
<p>Complete the square to state the coordinates of the vertex of each relation.</p><p><code class='latex inline'>y=4x^2-10x+1</code></p>
<p>Write each relation in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle y = 2x^2 + 10x + 8 </code></p>
<p>Write the relation in vertex form by completing the square.</p><p><code class='latex inline'>y=x^2+8x</code></p>
<p>Determine the maximum or minimum value of each relation by completing the square.</p><p> <code class='latex inline'>y=2.8x^2-33.6x+3.1</code></p>
<p>Determine the maximum or minimum value of each relation by completing the square.</p><p><code class='latex inline'>y=-10x^2+20x-5</code></p>
<p>Express each equation in factored form and vertex form.</p><p><code class='latex inline'>y = 4x^2 + 20x + 25</code></p>
<p>Graph the parabola by completing the square. Label the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = x^2 + 6x + 4 </code></p>
<p>Use algebra tiles to rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p> <code class='latex inline'>y=x^2+2x+5</code></p>
<p>Rewrite each equation in vertex form.</p><p><code class='latex inline'>\displaystyle y = x^2 + 4x + 1 </code></p>
<ol> <li>Complete the square to determine the coordinates of the vertex. State if the</li> </ol> <p>vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=-5 x^{2}-10 x+3 </code></p>
<p>Rewrite each equation in vertex form.</p><p><code class='latex inline'>\displaystyle y=-x^{2}-2 x+3 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. Use algebra tiles or a diagram to support your solution.</p><p><code class='latex inline'>\displaystyle y = x^2 + 8x -7 </code></p>
<p>Determine the coordinates of the vertex of each relation.</p><p><code class='latex inline'>\displaystyle y = x^2 -10x + 24 </code></p>
<p>Find the zeros and the vertex of each parabola. Then, sketch its graph. Check your results with a graphing calculator.</p><p><code class='latex inline'>y=-4x^2-18x-8</code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>\displaystyle y=x^{2}-8 x-6 </code></p>
<ol> <li>Complete the square to determine the coordinates of the vertex. State if the</li> </ol> <p>vertex is a minimum or a maximum.</p><p><code class='latex inline'>\displaystyle f(x)=-\frac{2}{5} x^{2}-\frac{4}{5} x-\frac{7}{5} </code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}+7 x+11 </code></p>
<p>Find the <code class='latex inline'>x</code>-intercepts, the vertex, and the equation of the axis of symmetry of each quadratic relation. Then, sketch the parabola.</p><p><code class='latex inline'>y=x^2-2x+3</code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2+6x-1</code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = -\frac{1}{2}x^2 - x + \frac{3}{2}</code></p>
<p>Complete the square to express each relation in vertex form. Then graph the relation.</p><p><code class='latex inline'>y=-x^2+6x-1</code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>y = x^2 -9x - 9</code></p>
<p>Complete the square to express each relation in vertex form. Then describe the transformations that must be applied to the graph of <code class='latex inline'>y=x^2</code> to graph the relation.</p><p><code class='latex inline'>y=4x^2+16x+36</code></p>
<p>Use algebra tiles to rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p><code class='latex inline'>y=x^2+10x+7</code></p>
<p>Use the quadratic relation determined by <code class='latex inline'>y = x^2 + 4x - 21</code>.</p><p>a) Express the relation in factored form.</p><p>b) Determine the zeros and the vertex.</p><p>c) Sketch its graph.</p>
<p>Complete the square to determine the vertex of <code class='latex inline'>y=x^2+bx+c</code>.</p>
<p> Complete the square to express each quadratic relation in the form <code class='latex inline'>y = a(x-h)^2 + k</code>. Then, give the coordinates of the vertex.</p><p><code class='latex inline'>\displaystyle y = x^2 -10x -5 </code></p>
<p>Determine the maximum or minimum value. Use at least two different methods.</p><p><code class='latex inline'> \displaystyle y = x^2 - 4x - 1 </code></p>
<p>Complete the square to express each relation in vertex form. Then graph the relation.</p><p><code class='latex inline'>y=-0.5x^2-3x+4</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'>y=x^2-10x+20</code></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^2 - 8x + 16</code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>y = x^2 + 4x</code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p> <code class='latex inline'>y=x^2+10x+20</code></p>
<p>Complete the square to write each quadratic relation in vertex form.</p><p><code class='latex inline'>\displaystyle y = x^2 -20x + 95 </code></p>
<p>Complete the square.</p><p><code class='latex inline'> \displaystyle y = -2x^2 + 12x -11 </code></p>
<p>Complete the square to write each quadratic relation in vertex form.</p><p><code class='latex inline'>\displaystyle y = -4.9x^2-19.6x + 12 </code></p>
<p>Find the value of missing symbols.</p><img src="/qimages/21915" /><p><code class='latex inline'>\displaystyle y=4 x^{2}+24 x-15 </code></p><p><code class='latex inline'>\displaystyle y=4\left(x^{2}+\square x\right)-15 </code></p><p><code class='latex inline'>\displaystyle y=4\left(x^{2}+6 x+--1\right)-15 </code></p><p><code class='latex inline'>\displaystyle y=4\left[\left(x^{2}+6 x+\infty\right)-\varphi\right]-15 </code></p><p><code class='latex inline'>\displaystyle y=4(x+0)^{2}--15 </code></p><p><code class='latex inline'>\displaystyle y=4(x+0)^{2}-\star </code></p>
<p>A parabola has equation <code class='latex inline'>y=x^2-4x-12</code></p><p>Find the equation of the axis of symmetry, find the vertex, and draw the graph.</p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = -3x^2 + 6x + 1</code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>\displaystyle f(x)=x^{2}+13 x+2 </code></p>
<p>Write each relation in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle y = 2x^2 + 16x + 30 </code></p>
<p>Complete the square to express each relation in vertex form. Then graph the relation.</p><p><code class='latex inline'>y=2x^2+4x-2</code></p>
<ol> <li>Complete the square to determine the coordinates of the vertex. State if the</li> </ol> <p>vertex is a minimum or a maximum.</p><p> <code class='latex inline'>\displaystyle f(x)=\frac{3}{4} x^{2}-3 x+6 </code></p>
<p> Find the vertex of the following parabolas and state which parabola(with its vertex at the origin) it is congruent to. </p><p><code class='latex inline'>\displaystyle y = x^2 - 6x + 10 </code></p>
<p>Determine the maximum or minimum value of </p><p><code class='latex inline'>\displaystyle f(x) =x^2 -6x+2 </code></p>
<p>Find the vertex of each quadratic relation by completing the square.</p><p> <code class='latex inline'>y=x^2-6x+17</code></p>
<p>Complete the square to write each quadratic relation in vertex form.</p><p><code class='latex inline'>\displaystyle y = x^2 + 8x -2 </code></p>
<p>Determine the vertex of the quadratic relation <code class='latex inline'>y=2x^2-4x+5</code> by completing the square.</p>
<p>Rewrite each relation in the form <code class='latex inline'>y = a(x - h)^2 + k</code> by completing the square. Use algebra tiles or a diagram to support your solution.</p><p><code class='latex inline'>\displaystyle y =x^2 + 8x -7 </code></p>
<p>Express each equation in factored form and vertex form.</p><p><code class='latex inline'>y = -2x^2 + 24x - 64</code></p>
<p>Complete the square to express each relation in vertex form. Then describe the transformations that must be applied to the graph of <code class='latex inline'>y=x^2</code> to graph the relation.</p><p><code class='latex inline'>y=0.5x^2-4x-8</code></p>
<p>Determine the maximum or minimum value of </p><p><code class='latex inline'>\displaystyle f(x) = -2x^2 + 10x </code></p>
<p>Complete the square for each function.</p><p><code class='latex inline'>y = x^2 + 7x + 11</code></p>
<p>Graph the parabola by completing the square. Label the vertex, the axis of symmetry, and two other points.</p><p><code class='latex inline'>\displaystyle y = -x^2 + 8x -3 </code></p>
<p>Find the location of the vertex.</p><p><code class='latex inline'>\displaystyle y = -5x^2 - 15x - 32 </code></p>
<ol> <li>Complete the square to determine the coordinates of the vertex. State if the</li> </ol> <p>vertex is a minimum or a maximum.</p><p> <code class='latex inline'>\displaystyle f(x)=3 x^{2}-15 x+\frac{59}{4} </code></p>
<p> Find the vertex of the following parabolas and state which parabola(with its vertex at the origin) it is congruent to. </p><p><code class='latex inline'>\displaystyle y = -5x^2 - 20x - 30 </code></p>
<p>Rewrite each relation in the form <code class='latex inline'>y=a(x-h)^2+k</code> by completing the square.</p><p> <code class='latex inline'>y=x^2+2x-1</code></p>
<p>Complete the square to write each quadratic relation in vertex form.</p><p><code class='latex inline'>\displaystyle y = 2x^2 +10x -12 </code></p>
<p>Write each relation in vertex form by completing the square.</p><p><code class='latex inline'> \displaystyle y = -3x^2 + 9x -2 </code></p>
<p>Find the maximum or minimum point of each parabola by completing the square.</p><p><code class='latex inline'>y=1.5x^2+6x-7</code></p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = 2x^2 + 12x + 16</code></p>
<p>Find the vertex of <code class='latex inline'>y = -2x^2 -12x -19</code>.</p>
<p>Determine the vertex of each quadratic function by completing the square. State if the vertex is a minimum or maximum.</p><p><code class='latex inline'>f(x) = x^2 + 10x + 6</code></p>
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