afaa4095-7825-4283-b8a1-e0e2781298f0.html

<div class="os-raise-familysupport">
  <p><a href="https://k12.openstax.org/contents/raise/resources/60af6c0390582241321a4cecc5e9c5ec1603fcb3" target="_blank">Access the activity sheet</a> and provide copies to your students so they can complete the project.</p>
</div>
<p>In this culminating project, students integrate ideas from the unit. Students will use the fact that the shape made by water coming out of a jet or fountain can be modeled with a quadratic equation. Students will design a fountain with given criteria.</p>
<p>In the first activity, students work through a simplified example with one fountain and one jet. Students will think about what information is needed to write the equation. They can use a sketch to draw the path. Students decide on some reasonable measurements and write the equation. Understanding the use of the vertex form of a quadratic equation is helpful.</p>
<p>The second activity gives students an opportunity to design a fountain with three to five jets. Students are given certain measurements and criteria to meet to write the equation for paths of the jets. Students may present their equations and an explanation of what information they used and how they wrote the equation of the path of the jets.</p>
<br>
<h4>Project Activities</h4>
<ol>
  <li>Introduction to Fountain Design <strong>(10 minutes)</strong></li>
  <li>Designing a Fountain <strong>(40 minutes)</strong></li>
</ol>
<h4>Required Preparation</h4>
<ol>
  <li><a target="_blank" href="https://k12.openstax.org/contents/raise/resources/60af6c0390582241321a4cecc5e9c5ec1603fcb3">Provide copies of the activity sheet</a> for students to use to collect their thinking. </li>
  <li> Consider demonstrating how to use sliders in Desmos to adjust the parameters of a quadratic equation in vertex form. For example, if \(y=-a(x-h)^2+k\) is used to represent a generic quadratic that opens down, students can easily experiment with its shape by moving sliders on \(a\), \(h\), and \(k\). </li>
</ol>

<h4> Required Materials</h4>
<ol>
  <li> Project 7 Blackline Masters
    <ul>
      <li><a href="https://k12.openstax.org/contents/raise/resources/fccfca9cb811007ffddd49fada3fb5ec2c85ee32" target="_blank">Advice on Modeling</a></li>
      <li><a href="https://k12.openstax.org/contents/raise/resources/3f1c4066ea22c519c0cb5c7cf03678e249120c45" target="_blank">Designing a Fountain Rubric</a></li>
    </ul>
  </li>
  <li> Recommend making technology available. Having access to graphing technology will streamline the process of testing different equations </li>
</ol>

<table class="os-raise-textheavytable">
    <caption>Learning Objectives</caption>
    <thead>
      <tr>
        <th scope="col">Learning Goals (Teacher Facing)</th>
        <th scope="col">Learning Targets (Student Facing)</th>
      </tr>
    </thead>
    <tbody>
      <tr>
        <td>
<ul>
  <li> Use quadratic functions to solve a real-world problem. </li>
</ul>
 </td>
        <td>
<ul>
  <li> Use quadratic functions to solve a real-world problem. </li>
</ul>
</td>
      </tr>
    </tbody>
  </table>
<br>
<h4>Texas Essential Knowledge and Skills (TEKS)</h4>
<ul>
  <li>A1(A) apply mathematics to problems arising in everyday life, society, and the workplace</li>
  <li>A1(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution</li>
  <li>A1(C) select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems</li>
  <li>A1(D) communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate</li>
  <li>A1(E) create and use representations to organize, record, and communicate mathematical ideas</li>
  <li>A1(F) analyze mathematical relationships to connect and communicate mathematical ideas</li>
  <li>A1(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.&nbsp; </li>
  <li> A6(B) write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form \((f(x)=a(x-h)^2+k)\), and rewrite the equation from vertex form to standard form \((f(x)=ax^2+bx+c\)); and </li>
  <li> A7(A) graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including \(x\)-intercept, \(y\)-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry; </li>
  <li> A7(C) determine the effects on the graph of the parent function \(f(x)=x^2\) when \(f(x)\) is replaced by \(af(x)\), \(f(x)+d, f(x-c)\), f(bx) for specific values of \(a\), \(b\), \(c\), and \(d\). </li>
</ul>