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efcd3bd0-d02e-4436-8f40-d86b26f5cb81.html
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<h4>Activity </h4>
<br>
<div class="os-raise-familysupport">
<p>Access the <a href="https://k12.openstax.org/contents/raise/resources/ad776e2f4b03a08bf69ddddc59a1efd31551b1a0" target="_blank">Desmos guide PDF</a> for tips on solving problems with the Desmos graphing calculator.</p>
</div>
<br>
<p>For questions 1 - 2, write an equation in vertex form of the quadratic function that has a vertex at (5, 8) and also goes through the point \((-3, 6)\).</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="7c4b2fdf-99bf-45be-bb4a-e1fc0017cb48" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#1-->
<div class="os-raise-ib-pset-problem" data-content-id="58610f1c-5083-4788-b112-383c4e6b3229" data-problem-comparator="text" data-problem-type="input" data-solution="-1/32">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li> Find the value of \(a\) for vertex form. </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
<p> \(y=a(x-h)^2+k\)<br>
\(6=a(-3-5)^2+8\)<br>
\(6=a(-8)^2+8\)<br>
\(-2=64a\)<br>
\(a=\frac{-2}{64}=\frac{-1}{32}\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \(\frac{-1}{32}\).</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>
<!--Q#2-->
<!--Q#2-->
<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="2">
<li> Write the equation in vertex form. </li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Enter your answer here and 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>\(y=\frac{-1}{32}(x-5)^2+8\)</p>
</div>
<br>
<p>For questions 3 and 4, write an equation in vertex form of the quadratic function that has a vertex at \((-4, 3)\) and also goes through the point \((2, 5)\).</p>
<!--Interaction End -->
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="97eef87e-235a-4e29-8ff0-039ad9c43c13" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#1-->
<div class="os-raise-ib-pset-problem" data-content-id="3fb8876e-eb1f-4f46-99ef-2345f1eefa1b" data-problem-comparator="text" data-problem-type="input" data-solution="1/18">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li> Find the value of \(a\) for vertex form. </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
<p> \(y=a(x-h)^2+k\)<br>
\(5=a(2-(-4))^2+3\)<br>
\(5=a(6)^2+3\)<br>
\(2=36a\)<br>
\(a=\frac{2}{36}=\frac{1}{18}\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \(\frac{1}{18}\).</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>
<!--Q#4-->
<!--Q#4-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="4">
<li> Write the equation in vertex form. </li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Enter your answer here and 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="Reveal2">
<p>Compare your answer:</p>
<p>\(y=\frac{1}{18}(x+4)^2+3\)</p>
</div>
<br>
<!--Interaction End -->
<br>
<p>For questions 5 - 6, write an equation in vertex form of the quadratic function that has a vertex at \((6, -2)\) and also goes through the point \((3, 1)\).</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="acc6b98f-0cd2-4418-8a4f-fdfdb625e5c3" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"><!--Q#5-->
<div class="os-raise-ib-pset-problem" data-content-id="672d6cf9-11c0-41b0-8896-377ea42f89d5" data-problem-comparator="text" data-problem-type="input" data-solution="1/3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li> Find the value of \(a\) for vertex form. </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
<p> \(y=a(x-h)^2+k\)<br>
\(1=a(3-6)^2+(-2)\)<br>
\(1=a(-3)^2-2\)<br>
\(3=9a\)<br>
\(a=\frac{3}{9}=\frac{1}{3}\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Nice try! The correct answer is \(\frac{1}{3}\).</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>
<!--Q#6-->
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal3" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="6">
<li> Write the equation in vertex form. </li>
</ol>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Enter your answer here and 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="Reveal3">
<p>Compare your answer:</p>
<p>\(y=\frac{1}{3}(x-6)^2-2\)</p>
</div>
<br>
<!--Interaction End -->
<br>
<br>
<h4>Video: Writing an Quadratic Equation from a Vertex and a Point</h4>
<p>Watch the following video to learn more about writing a quadratic equation from a vertex and a point.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><iframe allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" allowfullscreen frameborder="0" src="https://www.youtube-nocookie.com/embed/1IUEVwIjywc?si=lbcWBG5YBlTAOW1k;&rel=0" title="YouTube video player"></iframe></div>
</div>
<br>
<br>