340f0b49-6ef4-4abb-ab7a-3b0e31a3ab71.html

<h4>Quadratics Without Linear Terms</h4>
<p><strong>Example</strong></p>
<p>Find the \(x\)-intercepts and the vertex for \(f(x)=x^2-4\).</p>
<p><strong>Step 1</strong> - Write the function in factored form. Use difference of squares:</p>
<p>\(f(x)=x^2-4=(x-2)(x+2)\)</p>
<p><strong>Step 2</strong> - Set each factor equal to 0.</p>
<p>\(x - 2 = 0\)<br>
  \(x = 2\)</p>
<p>\(x + 2 = 0\)<br>
  \(x = -2\)</p>
<p>The \(x\)-intercepts are \((2, 0)\) and \((-2, 0)\).</p>
<p><strong>Step 3</strong> - Find the \(x\)-value in the middle of the two \(x\)-intercepts.
  This occurs at \(x = 0\). This is the \(x\)-coordinate of the vertex.</p>
<p> To find the point at the vertex, substitute into the function:<br>
  \(f(0)=0^2-4=-4\)</p>
<p>Vertex: \((0, -4)\)</p>
<h4>Try It: Quadratics Without Linear Terms</h4>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1" data-schema-version="1.0">
  <div class="os-raise-ib-cta-content">
    <p>Find the \(x\)-intercepts and the vertex for \(f(x)=x^2-64\).</p>
  </div>
  <div class="os-raise-ib-cta-prompt">
    <p>Write down your answers, then select the <strong>solution</strong> button to compare your work. </p>
  </div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1">
  <p>Here is how to find the \(x\)-intercepts and vertex of \(f(x)=x^2-64\):</p>
  <p><strong>Step 1</strong> - Write the function in factored form:<br>
    \(f(x)=x^2-64=(x-8)(x+8)\)</p>
  <p><strong>Step 2</strong> - Set each factor equal to 0.<br>
    \(x - 8 = 0\)<br>
    \(x = 8\)</p>
  <p>\(x + 8 = 0\)<br>
    \(x = -8\)</p>
  <p>The \(x\)-intercepts are at \((8, 0)\) and \((-8, 0)\).</p>
  <p>The vertex is located halfway between the \(x\)-intercepts, at \(x = 0\).</p>
  <p><strong>Step 3</strong> - To find the point, substitute into \(f(x)=x^2-64\).</p>
  <p>\(f(0)=0^2-64=-64\)</p>
  <p>The vertex is at \((0, -64)\).</p>
</div>