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33a4f041-f90f-46d6-9250-34ba32463d63.html
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<h4>Cool Down Activity</h4>
<p>In this lesson, you have learned how to write a quadratic function from different starting contexts and when provided different information.</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5ad9c7ae-136e-4859-871f-c347329e8698" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent">
<li>Identify a quadratic function in standard form, \(b(x)\), with the zeros –6 and 8.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter a quadratic function in standard form, \(b(x)\).</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(b(x) = x^2 − 2x − 48\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="39b14b68-ec8e-404b-9566-3a0251cae239" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Identify a quadratic function in standard form, \(m(x)\), with the given zero.</li>
</ol>
<p><img alt="A PARABOLA THAT OPENS UP WITH AN \(x\)-intercepts OF 6." height="393" src="https://k12.openstax.org/contents/raise/resources/b3c2e79ea248f2e456cd3375fb701cf47b884168" width="393"></p>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter a quadratic function in standard form, \(m(x)\).</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(m(x) = x^2 − 12x + 36\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="e13d7374-6f97-4a50-a731-8e8fce95b64e" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Write the specific quadratic function, \(d(x)\), in standard form, that has the zeros 2 and 5 and passes through the point \((1, 16)\).</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter the quadratic function, \(d(x)\), in standard form.</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>Intercept form: \(d(x) = a(x − 2)(x − 5)\)</p>
<p>Find the value of \(a\). Use point \((1, 16)\).</p>
<p>\(d(x) = a(x − 2)(x − 5)\)<br>
\(16 = a((1) − 2)((1) − 5)\)<br>
\(16 = a(-1)(-4)\)<br>
\(16 = 4a\)<br>
\(4 = a\)</p>
<p>Substitute 4 for \(a\).</p>
<p>\(d(x) = a(x − 2)(x − 5)\)<br>
\(d(x) = 4(x − 2)(x − 5)\)<br>
\(d(x) = 4(x^2 − 2x − 5x + 10)\)<br>
\(d(x) = 4(x^2 − 7x + 10)\)<br>
\(d(x) = 4x^2 − 28x + 40\)</p>
<p>So, the specific quadratic function written in standard form is \(d(x) = 4x^2 − 28x + 40\).</p>
</div>
</div>
<!--Interaction End -->