15825330-53fd-43cb-b344-9630bdc8d55b.html

<p><strong><em>Students will complete the following questions to practice the skills they have learned in this lesson.</em></strong></p>
<ol class="os-raise-noindent">
  <li>A quadratic function \(f\) is defined by \(f(x)=(x-7)(x+3)\).</li>
</ol>
<ol class="os-raise-noindent">
  <ol class="os-raise-noindent" type="a">
    <li> Without graphing, identify the \(x\)-intercepts of the graph of \(f\).
      <ul>
        <li> \((7,0),(-3,0)\) </li>
        <li> \((-7,0),(3,0)\) </li>
        <li> \((0,7),(0,-3)\) </li>
        <li> \((0,-7),(0,3)\) </li>
      </ul>
    </li>
  </ol>
</ol>
<p><strong>Answer:</strong> \((7,0),(-3,0)\). If \(x\) is 7, \((7-7)(7+3)\) gives (0,10), which is 0. &nbsp; If \(x\) is -3, \((-3-7)(-3+3)\) gives (-10,0), which is 0.</p>
<ol class="os-raise-noindent">
  <ol class="os-raise-noindent" start="2" type="a">
    <li> Use the standard form of \((x-7)(x+3)\) to identify the \(y\)-value of the \(y\)-intercept of the graph of \(f\).&nbsp; </li>
  </ol>
</ol>
<p><strong>Answer:</strong> &ndash; 21</p>
<ol class="os-raise-noindent" start="2">
  <li>Answer these questions for the equation \(y=x^2-5x+4\).</li>
</ol>
<ol class="os-raise-noindent">
  <ol class="os-raise-noindent" type="a">
    <li> What is the \(y\)-value of the \(y\)-intercept of this equation&rsquo;s graph? </li>
  </ol>
</ol>
<p><strong>Answer:</strong> 4</p>
<ol class="os-raise-noindent">
  <ol class="os-raise-noindent" start="2" type="a">
    <li> An equivalent way to write this equation is \(y=(x-4)(x-1)\). What are the \(x\)-intercepts of this equation&rsquo;s graph?
      <ul>
        <li> \((1,0),(4,0)\) </li>
        <li> \((-1,0),(-4,0)\) </li>
        <li> \((0,1),(0,4)\) </li>
        <li> \((0,-1),(0,-4)\) </li>
      </ul>
    </li>
  </ol>
</ol>
<p><strong>Answer:</strong> \((1,0),(4,0)\)</p>
<ol class="os-raise-noindent" start="3">
  <li>Noah said that if we graph \(y=(x-1)(x+6)\), the \(x\)-intercepts will be at \((1,0)\) and \((-6,0)\). Is Noah correct?
    <ul>
      <li> Yes </li>
      <li> No </li>
    </ul>
  </li>
</ol>
<p><strong>Answer: </strong>Yes. We can check by substituting 1 for \(x\) and -6 for \(x\) and see if they produce an output of 0. If \(x\) is 1, \((1-1)(1+6)\) gives (0)(7), which is 0. If \(x\) is &ndash; 6, \((-6-1)(-6+6)\) gives (-7)(0), which is 0.</p>
<ol class="os-raise-noindent" start="4">
  <li><strong>Select two</strong> \(x\)-intercepts of this graph.<br>
    <br>
    <img alt="A curve in an x y plane, origin O, with grid. Horizontal axis, scale negative 6 to 6, by 1&rsquo;s. Vertical axis, scale negative 8 to 8, by 1&rsquo;s. A curve passes through the points negative 1 comma 0, 1 comma negative 4, and 3 comma 0." height="195" src="https://k12.openstax.org/contents/raise/resources/6996d5bd6378e1a9f6b8fd7c0df4baa550e2ff48" width="268">
  </li>
</ol>
  <ul>
    <li> 1 </li>
    <li> -1 </li>
    <li> 3 </li>
    <li> -3 </li>
  </ul>

<p><strong>Answer:</strong> -1, 3</p>
<ol class="os-raise-noindent" start="5">
  <li>Use the standard form of \(y=(x-2)(x-4)\) to identify the \(y\)-value of the \(y\)-intercept of the graph.</li>
</ol>
<p><strong>Answer: </strong>8</p>