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<h4>Activity</h4>
<p>A function \(A\), defined by \(p(600−75p)\), describes the revenue collected from the sales of tickets for Performance A, a musical.</p>
<p>The graph represents a function \(B\) that models the revenue collected from the sales of tickets for Performance B, a Shakespearean comedy.</p>
<p><img height="215" src="https://k12.openstax.org/contents/raise/resources/d22a090d7b9a433cd29e770cec9c4f4058d70e5b" width="331"></p>
<p>In both functions, \(p\) represents the price of one ticket, and both revenues and prices are measured in dollars.</p>
<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">
<p>Without creating a graph of \(A\), determine which performance gives the greater <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">maximum</span> revenue when tickets are \(p\) dollars each. Explain or show your reasoning.</p>
</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>Performance A.</p>
<ul class="os-raise-noindent">
<li> The maximum revenue for Performance B is $900 based on the <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">vertex (of a graph)</span> of its graph. For Performance A, the expression \(p(600−75p)\) is in factored form, which tells us that the horizontal intercepts are \((0,0)\) and \((8,0)\). The horizontal coordinate of the vertex is halfway between 0 and 8, which is 4. Substituting 4 for \(p\) in \(p(600−75p)\) gives 1200, so the vertex is at \((4,1200)\). 1200 is greater than 900. </li>
<li> The maximum revenue for Performance B is $900 based on the vertex of its graph. The expression \(p(600−75p)\) can be rewritten in <span class="os-raise-ib-tooltip" data-schema-version="1.0" data-store="glossary-tooltip">vertex form (of a quadratic expression)</span>: \(-75(p−4)^2+1200\), which tells us that the vertex of a graph of the function is at \((4,1200)\) and that the maximum revenue is $1200. </li>
</ul>
</div>
<br>
<h4> Video: Comparing Maximums between Quadratics </h4>
<p>Watch the following video to learn more about comparing maximums between quadratics.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/d609275acd34998c8543a11b3df4e14a5a1343e8">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/0363bf355bdcd6bda581980f50acb0b0f068098e" srclang="en_us">https://k12.openstax.org/contents/raise/resources/d609275acd34998c8543a11b3df4e14a5a1343e8
</video></div>
</div>