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c3561bea-b1fd-4282-8755-405857bb6403.html
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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>
<ol class="os-raise-noindent">
<li>Here is the graph of quadratic function \(f\).</li>
</ol>
<p><img height="139" src="https://k12.openstax.org/contents/raise/resources/f6d2f05756f240bf0fbb2729b1726aedba9ccbb7" width="153"></p>
<p>Andre uses the expression \((x−5)^2+7\) to define \(f\).</p>
<p>Noah uses the expression \((x+5)^2−7\) to define \(f\).</p>
<p>Do you agree with either of them? </p>
<p><strong>Answer: </strong>No. The vertex of the graph is \((5,-7)\). The graph of Andre’s function would have a vertex at \((5,7)\), and the graph of Noah’s function would have a vertex at \((-5,-7)\).</p>
<ol class="os-raise-noindent" start="2">
<li>Here are the graphs of \(f(x)=x^2\), \(f(x)=x^2−5\), and \(f(x)=(x+2)^2−8\).</li>
</ol>
<p> <img height="219" src="https://k12.openstax.org/contents/raise/resources/b28e72de3d5826c42cdf5b308f3eff1a1537d56c" width="272"></p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" type="a">
<li> How do the three graphs compare?
<ul>
<li> They all have the same vertex. </li>
<li> The shape is the same but they are in different locations. </li>
<li> They all have a negative a coefficient in the vertex form of the equation. </li>
<li> All three graphs contain the point \((0,0)\). </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> The shape is the same but they are in different locations.</p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="2" type="a">
<li> Compare the graphs of \(f(x)=x^2\) and \(f(x)=x^2−5\). What role does the -5 play in the comparison?
<ul>
<li> Subtracting 5 from the squared term shifts the graph left by 5 units. </li>
<li> Subtracting 5 from the squared term shifts the graph right by 5 units. </li>
<li> Subtracting 5 from the squared term shifts the graph up by 5 units. </li>
<li> Subtracting 5 from the squared term shifts the graph down by 5 units. </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer:</strong> Subtracting 5 from the squared term shifts the graph down by 5 units.</p>
<ol class="os-raise-noindent">
<ol class="os-raise-noindent" start="3" type="a">
<li> Compare the graphs of \(f(x)=x^2\) and \(f(x)=(x+2)^2−8\). What roles do the \(+2\) and \(-8\) play in the comparison?
<ul>
<li> Adding 2 to \(x\) before squaring shifts the graph of \(f(x)=x^2\) to the left by 2 units and subtracting 8 from the squared term shifts the graph down by 8 units. </li>
<li> Adding 2 to \(x\) before squaring shifts the graph of \(f(x)=x^2\) to the up by 2 units and subtracting 8 from the squared term shifts the graph left by 8 units. </li>
<li> Adding 2 to \(x\) before squaring shifts the graph of \(f(x)=x^2\) to the right by 2 units and subtracting 8 from the squared term shifts the graph up by 8 units. </li>
<li> Adding 2 to \(x\) before squaring shifts the graph of \(f(x)=x^2\) to the down by 2 units and subtracting 8 from the squared term shifts the graph right by 8 units. </li>
</ul>
</li>
</ol>
</ol>
<p><strong>Answer: </strong>Adding 2 to \(x\) before squaring shifts the graph of \(f(x)=x^2\) to the left by 2 units and subtracting 8 from the squared term shifts the graph down by 8 units.</p>
<ol class="os-raise-noindent" start="3">
<li>Select three equations with a graph whose vertex has both a positive \(x\) and a positive \(y\). </li>
</ol>
<ul>
<li> \(f(x)=x^2\) </li>
<li> \(f(x)=(x−1)^2\) </li>
<li> \(f(x)=(x−3)^2+2\)</li>
<li> \(f(x)=2(x−4)^2−5\) </li>
<li> \(f(x)=0.5(x+2)^2+6\) </li>
<li> \(f(x)=-(x−4)^2+3\) </li>
<li> \(f(x)=-2(x−3)^2+1\) </li>
</ul>
<p><strong>Answer:</strong> \(f(x)=(x−3)^2+2\), \(f(x)=-(x−4)^2+3\), \(f(x)=-2(x−3)^2+1\)</p>
<ol class="os-raise-noindent" start="4">
<li>Which equation represents the graph shown?<br>
<br>
<img alt="GRAPH OF A DOWNWARD PARABOLA WITH A VERTEX AT (NEGATIVE 7, 3" height="279" src="https://k12.openstax.org/contents/raise/resources/e4e10406bde154391ac0790d52a32789409c6a48" width="273"><br>
<br> </li>
</ol>
<ul>
<li>\(f(x)=-(x+7)^2+3\) </li>
<li> \(f(x)=-(x-7)^2+3\) </li>
<li> \(f(x)=(x+7)^2+3\) </li>
<li> \(f(x)=(x-7)^2+3\) </li>
</ul>
<p><strong>Answer:</strong> \(f(x)=-(x+7)^2+3\)</p>
<ol class="os-raise-noindent" start="5">
<li>The graph representing \(f(x)=x^2\) is shifted 4 units to the left, 16 units down, and flipped so it opens downward (reflects over the \(x\)-axis). Which equation defines the curve? </li>
</ol>
<ul>
<li> \(f(x)=(x+4)^2-16\) </li>
<li> \(f(x)=-(x-4)^2-16\) </li>
<li> \(f(x)=-(x+4)^2-16\) </li>
<li> \(f(x)=(x-4)^2-16\) </li>
</ul>
<p><strong>Answer:</strong> \(f(x)=-(x+4)^2-16\)</p>
<ol class="os-raise-noindent" start="6">
<li>The graph of \(f(x) = x^2\) is transformed by a horizontal dilation of \(\frac12\). What is the equation of the function that results from this translation? </li>
</ol>
<ul>
<li>\(f(x) =\frac 12 x^2\)</li>
<li>\(f(x) = x^2 + \frac12\)</li>
<li>\(f(x) = (x-\frac 12)^2\)</li>
<li>\(f(x) = (\frac12x)^2\) </li>
</ul>
<p><strong>Answer:</strong> \(f(x) = (\frac12x)^2\) </p>
<ol class="os-raise-noindent" start="7">
<li>A function \(g(x) = (2x)^2 - 5\) was transformed from the parent quadratic function. Which of the following answer choices describes the transformations that were applied? </li>
</ol>
<p>Select the<strong> two</strong> descriptions that apply.</p>
<ul>
<li>A horizontal shift 2 units to the right</li>
<li>A horizontal dilation by a factor of 2</li>
<li>A horizontal shift left 5 units</li>
<li>A vertical shift down 5 units</li>
<li>A vertical dilation by a factor of 2</li>
</ul>
<p><strong>Answer:</strong> A horizontal dilation by a factor of 2 and A vertical shift down 5 units</p>
<ol class="os-raise-noindent" start="8">
<li>Which of the following represents a function that has experienced a horizontal compression? </li>
</ol>
<ul>
<li>\(f(x) = (-1x)^2\)</li>
<li>\(f(x) = (\frac 15x)^2\)</li>
<li>\(f(x) = (\frac 52x)^2\)</li>
<li>\(f(x) = x^2\)</li>
</ul>
<p><strong>Answer:</strong> \(f(x) = (\frac 52x)^2\)</p>
<br>
<p> </p>