e0563e1c-beb2-468f-95f7-1edde4c870bf.html

<h4>Activity</h4>
<p>Mai is learning to create computer animation by programming. In one part of her animation, she uses a quadratic function to model the path of the main character, an animated peanut, jumping over a wall.</p>
<p><img height="301" src="https://k12.openstax.org/contents/raise/resources/0250370ba6ce91f28fddd3ccbf84c786f82ea604" width="452"></p>
<p>Mai uses the equation \(y=-0.1(x&minus;h)^2+k\) to represent the path of the jump. \(y\) represents the height of the peanut as a function of the horizontal distance it travels, \(x\).</p>
<p>On the screen, the base of the wall is located at \((22,0)\), with the top of the wall at \((22,4.5)\). The dashed curve in the picture shows the graph of one equation Mai tried, where the peanut fails to make it over the wall.</p>
<p><img height="207" src="https://k12.openstax.org/contents/raise/resources/312cbbfe4c145142e6004586cfa01b526d2431a1" width="436"></p>
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      <ol class="os-raise-noindent">
        <li>What is the value of \(h\) in this equation?</li>
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      <p>Enter your answer here:&nbsp;</p>
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    <div class="os-raise-ib-pset-correct-response">
      <p>Correct!</p>
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      <p>The correct answer is \(h=18\).</p>
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      <ol class="os-raise-noindent" start="2">
        <li>What is the value of \(k\) in this equation?</li>
      </ol>
      <p>Enter your answer here:&nbsp;</p>
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    <div class="os-raise-ib-pset-correct-response">
      <p>Correct!</p>
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    <div class="os-raise-ib-pset-attempts-exhausted-response">
      <p>The correct answer is \(k=5\).</p>
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<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="3">
      <li>Starting with Mai's equation, choose values for \(h\) and \(k\) that will guarantee the peanut stays on the screen but also makes it over the wall. Be prepared to explain your reasoning.</li>
    </ol>
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  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answer. Then select the <strong>solution</strong> button to compare your work. </p>
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<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Compare your Answer:</p>
  <ul>
    <li> Use 22 for \(h\). Because \(h\) is the \(x\)-coordinate of the highest point of the jump, if that point is directly over the wall and the \(k\)-value remains at 5, then the peanut would clear the wall. So the new equation would be \(y=-0.1(x&minus;22)^2+5\). </li>
    <li> Change the value of \(k\), which is the vertical coordinate of the vertex, to 7 so that the vertex is at \((18,7)\) and there is still enough vertical distance to clear the 4.5-unit-tall wall when \(x\) is 22. The new equation would be \(y=-0.1(x&minus;18)^2+7\). </li>
  </ul>
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<h4>Video: Changing the Parameters of a Quadratic Expression</h4>
<p>Watch the following video to learn more about changing the parameters of a quadratic expression.</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/a4be91cfbfb16a613beae737d9d5f6244d411ff1">
      <track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/cb1d85d44e2eec12a7281ced0790c932455dd000" srclang="en_us">https://k12.openstax.org/contents/raise/resources/a4be91cfbfb16a613beae737d9d5f6244d411ff1
    </video></div>
</div>