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69a7a75c-1d34-42a5-a90d-89600018b359.html
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<p>Complete the following questions to practice the skills you have learned in this lesson.</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="41495d20-c4fa-4f99-b895-52a4494b8104" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0"> <!--Q#1-->
<div class="os-raise-ib-pset-problem" data-content-id="73e4ba8b-5ba4-41b1-8314-aae3db1bcec7" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\((-4, 6)\)" data-solution-options='["\\((8, 22)\\)", "\\((0, 22)\\)", "\\((-4, 6)\\)", "\\((4, 6)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>Which of the following points is the vertex of the quadratic function \(f(x)=x^2+8x+22\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-4, 6)\)</p>
<p>\((\frac{b}{2})^2=(\frac{8}{2})^2=16\)<br>
\(f(x)=x^2+8x+16+22-16\)<br>
\(f(x)=(x+4)^2+6\)<br>
Vertex: \((-4, 6)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.9.1.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \((-4, 6)\). </p>
</div>
</div>
<!--END QUESTION.--> <!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<p>For questions 2–4, use the function \(f(x)=(x-4)(x+2)\).</p>
<br>
<!--Q#2-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="8585ee96-150f-4228-848f-ad2e0dccfa9c" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="2">
<li>Write the function in standard form. Use the "^" symbol to enter an exponent.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(f(x)=x^2-2x-8\)</p>
<p>\(f(x)=(x-4)(x+2)\)<br>
\(f(x)=x^2-4x+2x-8\)<br>
\(f(x)=x^2-2x-8\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#3-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="55fe7e4c-ebc6-43b7-96e9-5c03353479ae" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="3">
<li>Write the function from question 2 in vertex form. Use the "^" symbol to enter an exponent.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(f(x)=(x-1)^2-9\)</p>
<p>\(f(x)=x^2 - 2x + 1 - 8 - 1\)<br>
\(f(x)=(x^2 - 2x + 1) - 9\)<br>
\(f(x)=(x-1)^2 - 9\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#4-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="95479bf9-631e-4a04-ac3e-9a400994015d" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="4">
<li>Identify the vertex from question 3. Use the "^" symbol to enter an exponent.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p> \((1, -9)\)<br>
\(f(x)=(x-1)^2-9\)<br>
Vertex is \((1, -9)\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<p>For questions 5 - 6, write an equation in vertex form of the quadratic function that has a vertex at \((-4, 1)\) and also goes through the point \((6, -1)\).</p>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="f5e9b4a1-8214-4115-88b7-d427810fc1b5" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0"> <!--Q#5-->
<div class="os-raise-ib-pset-problem" data-content-id="1ed28060-bc51-4003-91db-cfee70fddd12" data-problem-comparator="text" data-problem-type="input" data-solution="-1/50">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>Find the value of \(a\) for vertex form in simplest form. Use the "^" symbol to enter an exponent.</li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
<p>\(\frac{-1}{50}\)</p>
<p>\(-1=a(6-(-4))^2+(1)\)<br>
\(-1=a(10)^2+1\)<br>
\(-2=100a\)<br>
\(a=\frac{-2}{100}=\frac{-1}{50}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.9.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(\frac{-1}{50}\). </p>
</div>
</div>
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q#6-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="5cb3fdfc-ced5-4ef0-ae95-b0c6c6541248" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="6">
<li>Write the equation in vertex form. Use the "^" symbol to enter an exponent.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(y=\frac{-1}{50}(x+4)^2+1\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="afc3edaf-66a8-4487-95fe-8b4d1bc66439" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0"> <!--Q#7-->
<div class="os-raise-ib-pset-problem" data-content-id="a801a69a-ce71-4fc4-8cf5-402892a8e844" data-problem-comparator="text" data-problem-type="input" data-solution="5/36">
<div class="os-raise-ib-pset-problem-content">
<p>For questions 7 and 8, write an equation in vertex form of the quadratic function that has a vertex at \((-2, -3)\) and also goes through the point \((4, 2)\). Use the "^" symbol to enter an exponent.</p>
<ol class="os-raise-noindent" start="7">
<li>Find the value of \(a\) for vertex form in simplest form.</li>
</ol>
<p>Enter your answer here.</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct!</p>
<p>\(\frac{5}{36}\)</p>
<p>\(2=a(4-(-2))^2+(-3)\)<br>
\(2=a(6)^2+(-3)\)<br>
\(2+3=36a+(-3)+3\)<br>
\(5=36a\)<br>
\(a=\frac{5}{36}\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.9.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is \(a=\frac{5}{36}\). </p>
</div>
</div>
<!--Do not edit below line.-->
<div class="os-raise-ib-pset-correct-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
<div class="os-raise-ib-pset-encourage-response">
<!-- INSERT ANY VALID HTML HERE -->
</div>
</div>
<br>
<!--Q#8-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="25dd1a17-d959-45a0-9466-755d9d347cff" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="8">
<li>Write the equation in vertex form. Use the "^" symbol to enter an exponent.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(y=\frac{5}{36}(x+2)^2-3\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<!--Q#9-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="0ea78142-8d2b-4f7c-ad07-60bf616e0e8c" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<p>For questions 9 - 10, use the function \(f(x)=x^2\) that is shifted to create the function \(g(x)\) that has a vertex at \((-4, 6)\). Use the "^" symbol to enter an exponent.</p>
<br>
<ol class="os-raise-noindent" start="9">
<li>Write \(g(x)\) in vertex form.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(g(x)=(x+4)^2+6\)</p>
<p>Substitute the vertex in for \((h, k)\) <br>
\(g(x)=(x-(-4))^2+6\) <br>
\(g(x)=(x+4)^2+6\)</p>
</div>
</div>
<!--Interaction End -->
<br>
<br>
<!--Q#10-->
<div class="os-raise-ib-input" data-button-text="Solution" data-content-id="60bd9f86-e40b-4662-9244-1f9ad22d5935" data-fire-event="eventShow" data-schema-version="1.0">
<div class="os-raise-ib-input-content">
<ol class="os-raise-noindent" start="10">
<li> Write \(g(x)\) in standard form. Use the "^" symbol to enter an exponent.</li>
</ol>
</div>
<div class="os-raise-ib-input-prompt">
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-input-ack">
<p>Compare your answer:</p>
<p>\(g(x)=x^2+8x+22\)</p>
<p>Multiply the binomials then simplify.<br>
\(g(x)=(x+4)^2+6\)<br>
\(g(x)=(x+4)(x+4)+6\)<br>
\(g(x)=x^2+4x+4x+16+6\)<br>
\(g(x)=x^2+8x+22\)</p>
</div>
</div>
<!--Interaction End -->