fbfaa0b6-35dc-4e11-8b60-357937c490e2.html

<h4>Warm Up Activity</h4>
<ol class="os-raise-noindent">
  <li>Click on the "+" sign and choose to add a table in the Desmos graphing tool. This will generate a table for entering a data set.</li>
</ol>
<p>Desmos: Quadratic Data Set Table</p>
<div class="os-raise-ib-desmos-gc" data-bottom="-15" data-left="-2.5" data-right="7.5" data-schema-version="1.0" data-top="40"></div>
<ol class="os-raise-noindent" start="2">
  <li>Enter the data set shown in the table below into the corresponding \(x_1\) and \(y_1\) columns.&nbsp;</li>
</ol>
<p>(If preferred, the data can be copied and pasted into Desmos from a spreadsheet using keyboard shortcuts. Windows: Ctrl+C for copy and Ctrl+V for paste. Mac: Command+C for copy and Command+V for paste.)</p>
<table class="os-raise-skinnytable">
  <thead>
    <tr>
      <th scope="col"> \(x_1\) </th>
      <th scope="col"> \(y_1\) </th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td> 1 </td>
      <td> 2 </td>
    </tr>
    <tr>
      <td> 2 </td>
      <td> 5 </td>
    </tr>
    <tr>
      <td> 3 </td>
      <td> 10 </td>
    </tr>
    <tr>
      <td> 4 </td>
      <td> 17 </td>
    </tr>
    <tr>
      <td> 5 </td>
      <td> 26 </td>
    </tr>
  </tbody>
</table>
<br>
<p>The window should be appropriately set to display the points in the table, but sometimes it will be necessary to adjust the window of the graph in order to properly view your data set. Use the mouse to drag and change the viewing window. To zoom in or out, use the buttons in the top right or the scrolling wheel on the mouse.</p>
<!--Text Entry Interaction Start -->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="d4ca5fea-4940-4d21-bffe-b6a286beb0e2" data-fire-event="eventShow" data-schema-version="1.0">
  <div class="os-raise-ib-input-content">
    <ol class="os-raise-noindent" start="3">
      <li>Examine the data for a pattern that might fit any quadratic function that you recognize. What equation do you hypothesize would best fit these data points?</li>
    </ol>
  </div>
  <div class="os-raise-ib-input-prompt">
    <p>Enter an equation.</p>
  </div>
  <div class="os-raise-ib-input-ack">
    <p>Compare your answer:</p>
    <p>The data match the quadratic function \(y = x^2+ 1\).</p>
  </div>
</div>
<!--Interaction End -->
<br>
<p>In this lesson, we will learn to use technology to analyze a data set, find a curve of fit, and make predictions about a situation given the data that we have.</p>
<br>
<div class="os-raise-student-reflection">
  <p class="os-raise-student-reflection-title">Why Should I Care?</p>
  <img src="https://k12.openstax.org/contents/raise/resources/30e7516a84d6da9dd5ce800d5629baff748b26b3" width="400px"/>
  <p>Safe-Rain produces equipment for some pretty amazing fountains. Some of their fountains shoot jets of water that can form incredible visual displays and can be synchronized to music. </p>
  <p>The path of a jet of water can be modeled with a quadratic function. When Safe-Rain designs a new fountain, they use quadratic functions to plan precisely how high and far each jet of water will go. Without quadratic equations to guide it, the water would spray everywhere.</p>
</div>