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<p><strong><em>The following information can be shared with students' families to help support student engagement and encouragement at home.</em></strong></p>
<div class="os-raise-familysupport">
<p><a href="https://k12.openstax.org/contents/raise/resources/8db1fa60244125e32aa1928c4372e8e33788da53" target="_blank">Access the PDF version</a> of this page to share with parents or guardians. <a href="https://k12.openstax.org/contents/raise/resources/ccef0cebd03490eef3376bfdab9a6414369b3afd" target="_blank"> Spanish version available.</a></p>
</div>
<h4>Introduction to Quadratic Functions</h4>
<p>In this unit, students learn about quadratic functions. Earlier, they learned about linear functions that grow by repeatedly adding or subtracting the same amount and exponential functions that grow by repeatedly multiplying by the same amount.</p>
<p>Quadratic functions also change in a predictable way. Here, the number of small squares in each step is increasing by 3, then 5, then 7, and so on. How many squares are in Step 10? How many in Step n?</p>
<p><img height="125" src="https://k12.openstax.org/contents/raise/resources/b5cb1d6d3ed1a12a2636fe5d71174b1873787d97" width="312"></p>
<table class="os-raise-horizontaltable">
<caption>Here is a table that shows the pattern</caption>
<thead>
</thead>
<tbody>
<tr>
<th scope="row">Step number</th>
<td>1 </td>
<td>2 </td>
<td>3 </td>
<td>4 </td>
<td>10 </td>
<td>n </td>
</tr>
<tr>
<th scope="row">Number of small squares</th>
<td>1 </td>
<td>4 </td>
<td>9 </td>
<td>\(4 \cdot 4\) or 16 </td>
<td>\(10 \cdot 10\) or 100 </td>
<td>\(n \cdot n\) or \(n^2\) </td>
</tr>
</tbody>
</table>
<br>
<p>In this unit, students will also learn about some real-world situations that can be modeled by quadratic functions. <br><br>
For example, when you kick a ball up in the air, its distance above the ground as time passes can be modeled by a quadratic function. Study the graph below. The ball starts on the ground because the height is 0 when time is 0. The ball lands back on the ground after 2 seconds. After 1 second, the ball is 5 meters in the air.</p>
<p><img height="273" src="https://k12.openstax.org/contents/raise/resources/8e478f06fd9e94acea7a3ddf240bba1bfefb9cb6" width="313"></p>
<p>Both of the following expressions give the ball’s distance above the ground: \(5x(2−x)\) and \(10x−5x^2\), where \(x\) represents the number of seconds since it was kicked. Quadratic expressions are most recognizable when you can see the “squared term,” \(-5x^2\), as shown in \(10x−5x^2\).</p>
<p>Your student will learn even more about quadratics in the next two units.</p>
<h4>Apply</h4>
<p><strong>Try this task with your student</strong>
</p>
<p>The equation \(h=1+25t−5t^2\) models the height in meters of a model rocket \(t\) seconds after it is launched in the air. Here is a graph representing the equation.</p>
<p><img height="273" src="https://k12.openstax.org/contents/raise/resources/129f370c8ec5b030d93436d309b1f5991e8ef74d" width="315"></p>
<p><strong>Complete the following questions
</strong></p>
<ol class="os-raise-noindent">
<li> What was the approximate height of the rocket above the ground at the time it was launched? </li>
<li> About how high did it go into the air? </li>
<li> Approximately when did the rocket land back on the ground? </li>
</ol>
<p><strong>Hide the answers until you have attempted the questions
</strong></p>
<ol class="os-raise-noindent">
<li> 1 meter </li>
<li> about 32 meters </li>
<li> a little more than 5 seconds after launch </li>
</ol>
<h3>Review</h3>
<p><strong>Video lesson summaries for Unit 7: Introduction to Quadratic Functions</strong> <br> Each video highlights key concepts and vocabulary that students learn across one or more lessons in the unit. The content of these video lesson summaries is based on the written Lesson Summaries found at the end of the lessons in the curriculum. The goal of these videos is to support students in reviewing and checking their understanding of important concepts and vocabulary. </p>
</p><strong>Here are some possible ways families can use these videos</strong></p>
<ul>
<li> Keep informed on concepts and vocabulary students are learning about in class. </li>
<li> Watch with their students and pause at key points to predict what comes next or think up other examples of vocabulary terms. </li>
</ul>
<table class="os-raise-textheavyadjustedtable">
<thead>
<tr>
<th scope="col">Video Title</th>
<th scope="col">Related Lessons</th>
</tr>
</thead>
<tbody>
<tr>
<td><a href="https://www.youtube.com/watch?v=TEE28lo_2EY;&rel=0" target="_blank">Introducing Quadratic Functions</a></td>
<td>
<ul>
<li>Introduction to Quadratic Relationships</li>
<li>Building Quadratic Functions from Geometric Patterns</li>
<li>Comparing Quadratic and Exponential Functions</li>
</ul>
</td>
</tr>
<tr>
<td><a href="https://www.youtube.com/watch?v=ilb1wOZaOio;&rel=0" target="_blank">Building Quadratic Functions</a></td>
<td>
<ul>
<li>Building Quadratic Functions to Describe Situations, Part(s) 1 & 2</li>
<li>Domain, Range, Vertex, and Zeros of Quadratic Functions</li>
</ul>
</td>
</tr>
<tr>
<td><a href="https://www.youtube.com/watch?v=VU8rn-eIgSs;&rel=0" target="_blank">Working with Quadratic Expressions</a></td>
<td>
<ul>
<li>Equivalent Quadratic Expressions</li>
<li>Standard Form and Factored Form</li>
</ul>
</td>
</tr>
<tr>
<td><a href="https://www.youtube.com/watch?v=zb7OtVRR9B0;&rel=0" target="_blank">Graphing Quadratic Equations</a></td>
<td>
<ul>
<li>Graphs of Functions in Standard and Factored Form</li>
<li>Graphing from the Factored Form</li>
</ul>
</td>
</tr>
<tr>
<td><a href="https://www.youtube.com/watch?v=s_hsmVZwm1U;&rel=0" target="_blank">Graphing Standard Form</a></td>
<td>
<ul>
<li>Graphing the Standard Form, Part(s) 1 & 2</li>
<li>Graphs that Represent Situations</li>
</ul>
</td>
</tr>
<tr>
<td><a href="https://www.youtube.com/watch?v=E0vvqp7VFz0;&rel=0" target="_blank">Vertex Form</a></td>
<td>
<ul>
<li>Vertex Form</li>
<li>Graphing from the Vertex Form</li>
<li>Changing the Vertex</li>
</ul>
</td>
</tr>
</tbody>
</table>