7afb1f8d-c8e4-4065-a8ff-d2f3943ca1c1.html

<h4>Activity</h4>
<p>For questions 1 - 2, use the function \(f(x)=x^2\) that is shifted to create the function \(g(x)\) that has a vertex at \((3, -2)\).</p>
<ol class="os-raise-noindent">
  <li> Write \(g(x)\) in vertex form. </li>
</ol>
<p><strong>Answer:</strong> \(g(x)=(x-3)^2-2\)<br>
The vertex form of a quadratic is \(f(x)=a(x-h)^2+k\).<br>
Since there is not a vertical stretch or compression or reflection mentioned, the vertex values are substituted for \((h, k)\).<br>
\(g(x)=(x-3)^2+-2\) becomes \(g(x)=(x-3)^2-2\).</p>
<ol class="os-raise-noindent" start="2">
  <li> Write \(g(x)\) in standard form. </li>
</ol>
<p><strong>Answer:</strong> Compare your answer: \(g(x)=x^2-6x+7\)<br>
\(g(x)=(x-3)^2-2\)<br>
\(g(x)=(x-3)(x-3)-2\)<br>
\(g(x)=x^2-3x-3x+9-2\)<br>
\(g(x)=x^2-6x+7\)</p>
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<h4>Response to Student Thinking</h4>
<h5>More Chances</h5>
<p>Students will have more opportunities to understand the mathematical ideas in this cool down in 9.10, so there is no need to slow down or add additional work to the next lessons. Instead, use the results of this cool down to provide guidance for what to look for and emphasize over the next lesson to support students in advancing their current understanding.</p>