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<h4>Find the \(x\)-Intercepts</h4>
<p>The \(x\)-intercepts of the graph of an equation occur when \(y = 0\).</p>
<p><strong>Example 1</strong></p>
<p>For the equation \(y=(x-9)(x+2)\), look at the factors \((x-9)\) and \((x+2)\).<br>
Notice in the first factor, \((x-9)\), \(x=9\) makes the factor equal to 0.<br>
Substitute 9 for \(x\) in the equation.</p>
<p>\(y=(9-9)(9+2)\)<br>
\(y=(0)(11)\)<br>
\(y=0\)</p>
<p>Notice in the second factor, \((x+2)\), \(x=-2\) makes the factor equal to 0.<br>
Substitute -2 for \(x\) in the equation.</p>
<p>\(y=(-2-9)(-2+2)\)<br>
\(y=(-11)(0)\)<br>
\(y=0\)</p>
<p>In the equation \(y=(x-9)(x+2)\), \(y=0\) when \(x=9\) and \(x=-2\).<br>
The \(x\)-intercepts occur when \(x=9\) and \(x=-2\).<br>
To find the \(x\)-intercepts of a quadratic equation in factored form, set each factor equal to zero and solve for \(x\).</p>
<p><strong>Example 2</strong></p>
<p>Find the \(x\)-intercepts for \(y=(2x+7)(x-4)\).</p>
<p>The \(x\)-intercepts occur when \(y = 0\).<br>
Set each factor to 0 and solve.</p>
<p>\(\begin{array}{rcl}2x+7&=&0\;\;\;\;\;x-4&=&0\\x&=&-3.5\;\;\;\;\;\;x&=&4\end{array}\)</p>
<h4>Try It: Find the \(x\)-Intercepts</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 for \(y=(2x-5)(x+3)\).</p>
</div>
<div class="os-raise-ib-cta-prompt">
<p>Write down your answer, 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:</p>
<p>The \(x\)-intercepts occur when \(y = 0\).<br>
Set each factor to 0 and solve.</p>
<p>\(\begin{array}{rcl}2x-5&=&0\;\;\;\;\;x+3&=&0\\x&=&2.5\;\;\;\;\;\;x&=&-3\end{array}\)</p>
</div>
<h4>Check Your Understanding</h4>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="38be50d7-2d77-4cfd-87ad-c509b2f0e653" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0"> ----------------------------------------
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<div class="os-raise-ib-pset-problem" data-content-id="c70e3466-ddbb-46c7-8eb3-670add88a2bd" data-problem-type="multiplechoice" data-solution="\(x = 3\), \(x = -0.5\)" data-solution-options='["\\(x = -3\\), \\(x = 0.5\\)", "\\(x = 3\\), \\(x = -0.5\\)", "\\(x = -3\\), \\(x = 1\\)", "\\(x = 3\\), \\(x = -1\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<p>What are the \(x\)-intercept(s) of the graph of \(y=(2x+1)(x-3)\)?</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>Try again. Take a moment to think about what you learned in the mini-lesson review. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(x = 3\), \(x = -0.5\). </p>
</div>
</div>
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