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29cb0b8f-3c28-4049-85e4-c9aa35bcca05.html
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<h4>Cool Down Activity</h4>
<p>The function \(f\) is given by \(f(x)=(x-2)(x+4)\). </p>
<p>Without using graphing technology, answer questions 1–4.</p>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="67e7b0f7-d1af-43aa-a26f-c6a7ed14e169" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>What are the \(x\)-intercepts of the graph representing \(f\)? </li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p> \(x\)-intercepts for function \(f\): \((2,0)\) and \((-4,0)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="e3dc9f2d-934a-463e-938f-92d2a57cd2a8" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="3ef6b782-dbe3-4cae-a77c-9770e9a31299" data-problem-comparator="integer" data-problem-type="input" data-solution="-1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>What is the \(x\)-coordinate of the vertex of the graph?</li>
</ol>
<p>Enter your answer here:<strong><br></strong></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -1</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -1.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="9aa23552-aece-4c85-9209-34ffe324d66e" data-problem-comparator="integer" data-problem-type="input" data-solution="-9">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>What is the \(y\)-coordinate of the vertex of the graph?</li>
</ol>
<p>Enter your answer here:<strong><br></strong></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -9</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -9.</p>
</div>
</div>
<!--END QUESTION.-->
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="dd3bf0f2-541d-49a4-bd17-50ad807385f2" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>What is the \(y\)-intercept?</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p> The \(y\)-intercept is \((0,-8)\), because \((0-2)(0+4)=(-2)(4)=-8\).</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-desmos-gc" data-schema-version="1.0"></div>
<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="5">
<li>Use the graphing tool or technology outside the course. Sketch a graph that represents \(f\).</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Select the <strong>solution</strong> button to compare your work. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
<p>Compare your answer:</p>
<p>The graph opens upward with vertex at \((-1,-9)\) and \(x\)-intercepts at \((2,0)\) and \((-4, 0)\).</p>
<p><img alt="Graph on coordinate plane." height="267" src="https://k12.openstax.org/contents/raise/resources/881615b7474f3ba14c771ce12346fe82e703bc6d" width="262"></p>
</div>