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<p><strong><em>Students will complete the following questions to practice the skills they have learned in this lesson.</em></strong></p>
<ol class="os-raise-noindent">
<li><strong>Select two </strong>true statements about the graph that represents \(y=2x(x-11)\). </li>
</ol>
<ul>
<li> Its \(x\)-intercepts are at \((-2,0)\) and \((11,0)\). </li>
<li> Its \(x\)-intercepts are at \((0,0)\) and \((11,0)\). </li>
<li> Its \(x\)-intercepts are at \((2,0)\) and \((-11,0)\). </li>
<li> It has only one \(x\)-intercept. </li>
<li> The \(x\)-coordinate of its vertex is -4.5. </li>
<li> The \(x\)-coordinate of its vertex is 11. </li>
<li> The \(x\)-coordinate of its vertex is 4.5. </li>
<li> The \(x\)-coordinate of its vertex is 5.5. </li>
</ul>
<p><strong>Answer</strong>: Its \(x\)-intercepts are at \((0,0)\) and \((11,0)\). The \(x\)-coordinate of its vertex is 5.5.</p>
<ol class="os-raise-noindent" start="2">
<li><strong>Select two </strong>equations whose graphs have a vertex with \(x\)-coordinate 2. </li>
</ol>
<ul>
<li> \(y=(x-2)(x-4)\) </li>
<li> \(y=(x-2)(x+2)\) </li>
<li> \(y=(x-1)(x-3)\) </li>
<li> \(y=x(x+4)\) </li>
<li>\( y=x(x-4)\) </li>
</ul>
<p><strong>Answer:</strong> \(y=(x-1)(x-3)\), \(y=x(x-4)\)</p>
<ol class="os-raise-noindent" start="3">
<li>Three different equations are given. Refer to these equations to complete questions a–f.</li>
</ol>
<table class="os-raise-wideequaltable">
<thead>
<tr>
<th scope="col">Equation</th>
<th scope="col">\(x\)-intercept</th>
<th scope="col">\(x\)-coordinate of the vertex</th>
</tr>
</thead>
<tbody>
<tr>
<td>
<p>\(y=x(x-2)\)</p>
</td>
<td>
<p>a. _____</p>
</td>
<td>
<p>b. _____</p>
</td>
</tr>
<tr>
<td>
<p>\(y=(x-4)(x+5)\)</p>
</td>
<td>
<p>c. _____</p>
</td>
<td>
<p>d. _____</p>
</td>
</tr>
<tr>
<td>
<p>\(y=-5x(3-x)\)</p>
</td>
<td>
<p>e. _____</p>
</td>
<td>
<p>f. _____</p>
</td>
</tr>
</tbody>
</table>
<br>
<ol class="os-raise-noindent" type="a">
<li> What are the \(x\)-intercepts of the graph that represents \(y=x(x-2)\)? </li>
</ol>
<ul>
<li>\((0,0)\) and \((0, 2)\) </li>
<li> \((0,0)\) and \((2, 0)\) </li>
<li>\((0,0)\) and \((0,-2)\) </li>
<li> \((0,0)\) and \((-2,0)\) </li>
</ul>
<p><strong>Answer:</strong> \((0,0)\) and \((2,0)\)</p>
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the \(x\)-coordinate of the vertex of the graph that represents \(y=x(x-2)\)? </li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> What are the \(x\)-intercepts of the graph that represents \(y=(x-4)(x+5)\)?
<ul>
<li>\((-5,0)\) and \((4,0)\) </li>
<li> \((0,-5)\) and \((0,4)\) </li>
<li> \((5,0)\) and \((-4,0)\) </li>
<li> \((0,5)\) and \((0,-4)\) </li>
</ul>
</li>
</ol>
<p><strong>Answer:</strong> \((-5,0)\) and \((4,0)\)</p>
<ol class="os-raise-noindent" start="4" type="a">
<li> What is the \(x\)-coordinate of the vertex of the graph that represents \(y=(x-4)(x+5)\)? </li>
</ol>
<p><strong>Answer:</strong> -0.5</p>
<ol class="os-raise-noindent" start="5" type="a">
<li> What are the \(x\)-intercepts of the graph that represents \(y=-5x(3-x)\)? </li>
</ol>
<ul>
<li>\((0,0)\) and \((0,-3)\) </li>
<li>\((0,0)\) and \((-3,0)\) </li>
<li>\((0,0)\) and \((3,0)\) </li>
<li> \((0,0)\) and \((0,3)\) </li>
</ul>
<p><strong>Answer:</strong> \((0,0)\) and \((3,0)\)</p>
<ol class="os-raise-noindent" start="6" type="a">
<li> What is the \(x\)-coordinate of the vertex of the graph that represents \(y=-5x(3-x)\)? </li>
</ol>
<p><strong>Answer:</strong> 1.5</p>
<ol class="os-raise-noindent" start="4">
<li>What is the equation of the axis of symmetry of \(y = (x - 4)(x + 5)\)? (If needed, enter fractional values as a decimal.)
</li>
</ol>
<p><strong>Answer:</strong> -0.5</p>
<ol class="os-raise-noindent" start="5">
<li>Answer questions a–c about the function \(y=(x-2)(x-4)\).</li>
</ol>
<ul>
</ul>
<ol class="os-raise-noindent" type="a">
<li> What are the \(x\)-intercepts of the graph of \(y=(x-2)(x-4)\)? </li>
</ol>
<ul>
<li> \((2,0)\) and \((4,0)\) </li>
<li> \((0,2)\) and \((0,4)\) </li>
<li> \((-2,0)\) and \((-4,0)\) </li>
<li> \((0,-2)\) and \((0,-4)\) </li>
</ul>
<p><strong>Answer:</strong> \((2,0)\) and \((4,0)\)</p>
<ul>
</ul>
<ol class="os-raise-noindent" start="2" type="a">
<li> Is \((-1,3)\) a point on the graph? </li>
</ol>
<ul>
<li> Yes </li>
<li> No </li>
</ul>
<p><strong>Answer: </strong>No. Substituting -1 for \(x\) gives \((-1-2)(-1-4)\) or \(-3 \cdot -5\), which is 15, so \((-1,15)\) would be a point on the graph, not \((-1,3)\).</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> Does the graph represent the equation \(y=(x-2)(x-4)\)? <br>
<br>
<img alt="Graph of nonlinear function, origin O. Horizontal axis from negative 8 to 6, by 2’s. Vertical axis from negative 8 to 12, by 4’s. Line passes through negative 7 comma 8, negative 5 comma 0, negative 3 comma 0 and 1 comma 7." height="171" src="https://k12.openstax.org/contents/raise/resources/4d7ede3e12cc95715ca6ed8c75079c4081888c1a" width="262">
</li>
</ol>
<ul>
<li> Yes </li>
<li> No </li>
</ul>
<p><strong>Answer:</strong> No</p>