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19fa6350-b069-42fc-96d2-75b7645c9609.html
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<h4>Cool Down Activity</h4>
<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">
<li>Without graphing, find the <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">vertex (of a graph)</span> of the graph of a quadratic function defined by \(f(x)=-x^2−14x−60\). Show your reasoning.</li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, then 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 vertex is at \((-7,-11)\).</p>
<p>\(f(x)=-(x^2+14x+60)\)</p>
<p>\(f(x)=-(x^2+14x+49+11)\)</p>
<p>\(f(x)=-((x+7)^2+11)\)</p>
<p>\(f(x)=-(x+7)^2−11\)</p>
</div>
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d14411ee-3af2-4478-90c3-02e6b2fb9a0f" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Does the \(y\)-coordinate of the vertex correspond to a <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">maximum</span> or a <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">minimum</span> value of the function? Explain how you know.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your explanation. </p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>A maximum value. The squared term has a coefficient of -1. The squared term will be 0 when \(x\) is -7. For all other values of \(x\), the squared term will be subtracted from -11, resulting in outputs that are less than -11.</p>
</div>
</div>
<!--Interaction End -->
<p><strong>Note:</strong> If the vertex isn't asked for and the "value of the maximum or minimum" is asked for, the maximum or minimum value occurs at the \(y\)-value of the vertex because that is the value of the coordinate that represents the vertical height of the point.</p>