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<p><strong><em>Students will complete the following questions to practice the skills they have learned in this lesson.</em></strong></p>
<p>For each equation in questions 1–5, identify the values of \(a\), \(b\), and \(c\) that you would substitute into the quadratic formula to solve the equation.</p>
<ol class="os-raise-noindent">
<li>\(3x^2+8x+4=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 3</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 8</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> 4</p>
<ol class="os-raise-noindent" start="2">
<li>\(2x^2−5x+2=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 2</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> -5</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> 2</p>
<ol class="os-raise-noindent" start="3">
<li>\(-9x^2+13x−1=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> -9</p>
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 13</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> -1</p>
<ol class="os-raise-noindent" start="4">
<li>\(x^2+x−11=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> -11</p>
<ol class="os-raise-noindent" start="5">
<li>\(-x^2+16x+64=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> -1</p>
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 16</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> 64</p>
<ol class="os-raise-noindent" start="6">
<li>For each equation, use the quadratic formula to solve the equation, then choose the correct <strong>two </strong>solutions for \(x\). </li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>\(x^2+9x+20=0\)</li>
</ol>
<ul class="os-raise-noindent">
<li> 4 </li>
<li> -4 </li>
<li> -5 </li>
<li> 5 </li>
<li> 1 </li>
<li> 9 </li>
<li> 20 </li>
</ul>
<p><strong>Answer:</strong> -4, -5</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>\(x^2−10x+21=0\)</li>
</ol>
<ul class="os-raise-noindent">
<li> 3 </li>
<li> -7 </li>
<li> 21 </li>
<li> -10 </li>
<li> 1 </li>
<li> -4 </li>
<li> 7 </li>
</ul>
<p><strong>Answer:</strong> 3, 7</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>\(3x^2−5x+1=0\)</li>
</ol>
<ul class="os-raise-noindent">
<li>\(\frac{13}{6}+\frac{\sqrt{5}}{6}\)</li>
<li> -1 </li>
<li>\(\frac{5}{6}-\frac{\sqrt{13}}{6}\)</li>
<li>\(\frac{13}{6}-\frac{\sqrt{5}}{6}\)</li>
<li>\(-\frac{18}{6}-3\)</li>
<li>\(\frac{5}{6}+\frac{\sqrt{13}}{6}\)</li>
<li>\(\frac{18}{6}-3\)</li>
</ul>
<p><strong>Answer:</strong>\(\frac{5}{6}+\frac{\sqrt{13}}{6}\), \(\frac{5}{6}-\frac{\sqrt{13}}{6}\)</p>
<p>For each equation for questions 7–12, identify the values of \(a\), \(b\), and \(c\) that you would substitute into the quadratic formula to solve the equation.</p>
<ol class="os-raise-noindent" start="7">
<li>\(x^2+9x+18=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li> What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 9</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> 18</p>
<ol class="os-raise-noindent" start="8">
<li>\(4x^2−3x+11=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>a. What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 4</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> -3</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> 11</p>
<ol class="os-raise-noindent" start="9">
<li>\(81−x+5x^2=0\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li> What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 5</p>
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> -1</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> 81</p>
<ol class="os-raise-noindent" start="10">
<li>\(45x^2+3x=\frac{1}{3}\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 45</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 3</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>What is the value of \(c\)?</li>
</ol>
<ul class="os-raise-noindent">
<li>\(-\frac{1}{3}\)</li>
<li> \(\frac{1}{3}\)</li>
<li> 1 </li>
<li> 0 </li>
</ul>
<p><strong>Answer:</strong>\(-\frac{1}{3}\)</p>
<ol class="os-raise-noindent" start="11">
<li>\(121=x^2\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li>What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 1</p>
<ol class="os-raise-noindent" start="2" type="a">
<li>What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 0</p>
<ol class="os-raise-noindent" start="3" type="a">
<li>What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> -121</p>
<ol class="os-raise-noindent" start="12">
<li>\(7x+14x^2=42\)</li>
</ol>
<ol class="os-raise-noindent" type="a">
<li> What is the value of \(a\)?</li>
</ol>
<p><strong>Answer:</strong> 14</p>
<ol class="os-raise-noindent" start="2" type="a">
<li> What is the value of \(b\)?</li>
</ol>
<p><strong>Answer:</strong> 7</p>
<ol class="os-raise-noindent" start="3" type="a">
<li> What is the value of \(c\)?</li>
</ol>
<p><strong>Answer:</strong> -42</p>