Now You Try

<p>Solve. Round answers to the nearest hundredth, where necessary.</p><p> <code class='latex inline'>(x-3)^2=-2(x+3)</code></p>

<p>Determine the roots of <code class='latex inline'>x^2-6x+5=0</code> by using the quadratic formula and by factoring.</p>

<p>Use the quadratic formula to solve each equation. Express answers as exact roots.</p><p><code class='latex inline'>4x^2-12x+9=0</code></p>

<p>Use the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. Verify graphically with technology.</p><p><code class='latex inline'>3x^2+14x+5=0</code></p>

<p>For each quadratic relation, state the coordinates of the vertex and the direction of opening. Then, determine how many <code class='latex inline'>x</code>-intercepts the relation has.</p><p><code class='latex inline'>y=2(x+4)^2-5</code></p>

<p>Use the quadratic formula to solve each equation. Express answers as exact roots.</p><p><code class='latex inline'>2x^2-7x=-4</code></p>

<p>Use the quadratic formula to solve each equation. Express answers as exact roots.</p><p><code class='latex inline'>2x^2+4x-7=0</code></p>

<p>Solve. Round answers to the nearest hundredth, where necessary.</p><p><code class='latex inline'>(x+3)^2=(2x+5)(2x-5)</code></p>

<p>Solve. Round answers to the nearest hundredth, where necessary.</p><p><code class='latex inline'>4x^2=12-13x</code></p>

<p>The shape of the Humber River pedestrian bridge in Toronto can be modelled by the equation <code class='latex inline'>y=-0.0044x^2+21.3</code>. All measurements are in metres. Determine the length of the bridge and the maximum height above the ground, to the nearest tenth of a metre.</p>

<p>Show that the roots of</p><p><code class='latex inline'>x = 1 + \frac{1}{x}</code> are negative reciprocals. </p>

<p>Use the quadratic formula to solve each equation. Express answers as exact roots.</p><p><code class='latex inline'>3x^2+5x=1</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>For each quadratic relation, state the coordinates of the vertex and the direction of opening. Then, determine how many <code class='latex inline'>x</code>-intercepts the relation has.</p><p> <code class='latex inline'>y=-(x-2)^2+4</code></p>

<p>Use the quadratic formula to solve each equation. Express answers as exact roots.</p><p><code class='latex inline'>7x^2+24x+9=0</code></p>

<p>Find a quadratic equation with each pair of roots.</p><p><code class='latex inline'>\displaystyle{x=\frac{15\pm\sqrt{140}}{4}}</code></p>

<p>The platforms on the ends of the half-pipe are at the same height. </p><img src="/qimages/1118" /><p>a) How wide is the half-pipe?</p>

<p>Which method would you use to solve each equation? Justify your choice. Then, solve. Do any of your answers suggest that you might have used another method? Explain.</p><p><code class='latex inline'>0.57x^2 - 3.7x - 2.5 = 0</code></p>

<p>Write an equation of a parabola, in the form <code class='latex inline'>y=a(x-h)^2+k</code>, satisfying each description. Then, write each relation in the form <code class='latex inline'>y=ax^2+bx+c</code> Use graphing technology or the quadratic formula to verify that your equation satisfies the description.</p>
<ul>
<li>no <code class='latex inline'>x</code>-intercept</li>
</ul>

<p>A toy rocket is launched from a <code class='latex inline'>3</code>-m platform, at <code class='latex inline'>8.1</code> m/s. The height of the rocket is modelled by the equation <code class='latex inline'>h=-4.9t^2+8.1t+3</code>,where <code class='latex inline'>h</code> is the height, in metres, above the ground and <code class='latex inline'>t</code> is the time, in seconds.</p><p>a) After how many seconds will the rocket rise to a height of 6 m above the ground? Round your answer to the nearest hundredth.</p><p>b) When does the rocket fall again to a height of 6 m above the ground? Use your answers from parts a] and b) to determine when the rocket reached its maximum height above the ground.</p><p><code class='latex inline'>\to</code> c) Use your answers from parts a] and b) to determine when the rocket reached its maximum height above the ground.</p>

<p>Write an equation of a parabola, in the form <code class='latex inline'>y=a(x-h)^2+k</code>, satisfying each description. Then, write each relation in the form <code class='latex inline'>y=ax^2+bx+c</code> Use graphing technology or the quadratic formula to verify that your equation satisfies the description.</p>
<ul>
<li>one <code class='latex inline'>x</code>-intercept </li>
</ul>

<p>Solve. Round answers to the nearest hundredth, where necessary.</p><p><code class='latex inline'>x(3x-8)=-1</code></p>

<p>What are the approximate solutions of the equation <code class='latex inline'>\displaystyle \frac{5}{2} x^{2}+\frac{3}{4} x-5=0 ? </code> Use a graphing calculator.</p><p><code class='latex inline'>\displaystyle \begin{array}{lll}\text { A }-5,0 & \text { (B) }-1.57,1.27 & \text { C }-1.36,0.71\end{array} </code> (D) <code class='latex inline'>\displaystyle -0.96,0.84 </code></p>

<p>se the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. Verify graphically with technology.</p><p><code class='latex inline'>-6x^2+17x+5=0</code></p>

<p>A toy rocket is launched from a 3-m platform, at <code class='latex inline'>8.1</code> m/s. The height of the rocket is modelled by the equation <code class='latex inline'>h=-4.9t^2+8.1t+3</code>,where <code class='latex inline'>h</code> is the height, in metres, above the ground and <code class='latex inline'>t</code> is the time, in seconds.</p><p>a) After how many seconds will the rocket rise to a height of 6 m above the ground? Round your answer to the nearest hundredth.</p><p>b) When does the rocket fall again to a height of 6 m above the ground? Use your answers from parts a] and b) to determine when the rocket reached its maximum height above the ground.</p>

<p>Solve. Round answers to the nearest hundredth, where necessary.</p><p><code class='latex inline'>4x^2=2.8x+4.8</code></p>

<p>se the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. Verify graphically with technology.</p><p><code class='latex inline'>-5x^2+16x-2=0</code></p>

<p>Solve each quadratic equation. Give exact answers.</p><p><code class='latex inline'>3x^2 -2x - 2=0</code></p>

<p>For each quadratic relation, state the coordinates of the vertex and the direction of opening. Then, determine how many <code class='latex inline'>x</code>-intercepts the relation has.</p><p><code class='latex inline'>y=(x-5)^2</code></p>

<p>se the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. Verify graphically with technology.</p><p><code class='latex inline'>10x^2-45x-7=0</code></p>

<p>Use the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. Verify graphically with technology.</p><p> <code class='latex inline'>4x^2-7x-1=0</code></p>

<p>Write an equation of a parabola, in the form <code class='latex inline'>y=a(x-h)^2+k</code>, satisfying each description. Then, write each relation in the form <code class='latex inline'>y=ax^2+bx+c</code> Use graphing technology or the quadratic formula to verify that your equation satisfies the description.</p>
<ul>
<li> two <code class='latex inline'>x</code>-intercepts </li>
</ul>

<p>Use the quadratic formula to solve each equation. Express answers as exact roots.</p><p><code class='latex inline'>16x^2+24x=-9</code></p>

<p>Use the quadratic formula to solve each equation. Express your answers as exact roots.</p><p><code class='latex inline'>\displaystyle
-3x^2 -2x + 5 = 0
</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+10x+25</code></p>

<p>se the quadratic formula to solve. Express your answers as exact roots and as approximate roots, rounded to the nearest hundredth. Verify graphically with technology.</p><p><code class='latex inline'>8x^2+12x+1=0</code></p>

<p>For each quadratic relation, state the coordinates of the vertex and the direction of opening. Then, determine how many <code class='latex inline'>x</code>-intercepts the relation has.</p><p> <code class='latex inline'>y=-2(x+3)^2-1</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=5x^2-14x-3</code></p>

<p>The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9 m by 6 m. The flower bed will be surrounded by a path of constant width with the same area as the flower bed. Calculate the perimeter of the outside of the path.</p><img src="/qimages/1878" /><p>a) Set up a quadratic equation to model the question.</p><p>b) Use the quadratic formula to solve the problem.</p><p>c) Check your solution using a graphing calculator.</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=9x^2-24x+16</code></p>

<p>The path of a soccer ball after it is kicked from a height of 0.5 m above the ground is given by the equation <code class='latex inline'>h=-0.1d^2+d+0.5</code>, where <code class='latex inline'>h</code> is the height. in metres, above the ground and <code class='latex inline'>d</code> is the horizontal distance, in metres. </p>
<ul>
<li> How far has the soccer ball travelled horizontally. to the nearest tenth of a metre, when it lands on the ground?</li>
</ul>

<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>For each quadratic relation, state the coordinates of the vertex and the direction of opening. Then, determine how many <code class='latex inline'>x</code>-intercepts the relation has.</p><p><code class='latex inline'>y=(x-3)^2+2</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=2x^2-5x-12</code></p>

<p>The platforms on the ends of the half-pipe are at the same height. </p><img src="/qimages/1118" /><p>a) How wide is the half-pipe?</p><p><code class='latex inline'>\to</code> b) How far would a skater have travelled horizontally after a drop of 2 m? Round to the nearest hundredth of a metre.</p>

<p>Solve. Round answers to the nearest hundredth, where necessary.</p><p><code class='latex inline'>7x^2-12x=9</code></p>