8618b6f5-328f-40f6-b455-2ba08a52c5ab.html

<h3>Warm Up (5 minutes)</h3>
<p>This warm up reminds students about features of the graph that are visible in the different forms of expressions defining a quadratic function.</p>
<h4>Launch</h4>
<p>Encourage and support opportunities for peer interactions. Invite students to talk about their ideas with a partner before writing them down.</p>
<h4>Student Activity</h4>
<p>These expressions each define the same function.</p>
<ul class="os-raise-noindent">
  <li> \(x^2+6x+8\) </li>
  <li> \((x+2)(x+4)\) </li>
  <li> \((x+3)^2&minus;1\) </li>
</ul>
<p>Without graphing or doing any calculations, determine where the following features would be on a graph that represents the function.</p>
<ol class="os-raise-noindent">
  <li>The \(x\)-coordinate of the vertex (of a graph).</li>
</ol>
<p><strong>Answer:</strong> -3</p>
<ol class="os-raise-noindent" start="2">
  <li>The \(y\)-coordinate of the vertex (of a graph).</li>
</ol>
<p><strong>Answer:</strong> -1</p>
<ol class="os-raise-noindent" start="3">
  <li><strong>Select both</strong> \(x\)-intercepts.</li>
</ol>
<ul class="os-raise-noindent">
  <li> \((-2,0)\) </li>
  <li> \((-6,0)\) </li>
  <li> \((-4,0)\) </li>
  <li> \((-8,0)\) </li>
</ul>
<p><strong>Answer:</strong> \((-2,0)\), \((-4,0)\)</p>
<ol class="os-raise-noindent" start="4">
  <li>The \(y\)-coordinate of the \(y\)-intercept \((0, \_\_\_\_\_)\)</li>
</ol>
<p><strong>Answer:</strong> 8<br>
  The \(y\)-intercept is \((0,8)\).</p>
<h4>Activity Synthesis</h4>
<p>Invite students to share how they would locate the specified features on a graph. Make sure students are reminded that:</p>
<ul class="os-raise-noindent">
  <li> The constant term in the standard form tells us the \(y\)-intercept. </li>
  <li> The factored form shows us the \(x\)-intercepts. </li>
  <li> The vertex form reveals the vertex. </li>
</ul>
<p>Consider using graphing technology to demonstrate that the three expressions appear to produce the same graph. (We can verify algebraically that the three expressions define the same function, but we can't be sure that the three expressions define the same function just by looking at the graph.) Label the vertex, \(x\)-intercepts, and \(y\)-intercept.</p>