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725633a3-f303-40cd-9f95-b997f750a8c9.html
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<!--Do not edit this div tag. It must surround the interaction block-->
<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="cfbe1b75-2465-4e60-a1b3-388b6e74600f" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--1a-->
<div class="os-raise-ib-pset-problem" data-content-id="74779890-74be-4c6e-abac-e9c6c8418736" data-problem-comparator="integer" data-problem-type="input" data-solution="9">
<div class="os-raise-ib-pset-problem-content">
<p>For questions 1 - 5, the standard form</p>
<ol class="os-raise-noindent">
<li>The standard form of an equation is \(ax^2+bx+c\). For each expression, find the missing constant \(c\) that would make the expression a perfect square.</li>
</ol>
<p>\(x^2−6x+ \underline{\;\;c\;\;}\)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 9 can be added to make the expression a perfect square.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: 9 can be added to make the expression a perfect square. </p>
</div>
</div>
<!--1b-->
<div class="os-raise-ib-pset-problem" data-content-id="aff55de0-7356-4328-86a8-3cef24731e96" data-problem-comparator="integer" data-problem-type="input" data-solution="1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" >
<li>\(x^2+2x+ \underline{\;\;c\;\;}\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 1 can be added to make the expression a perfect square.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: 1 can be added to make the expression a perfect square. </p>
</div>
</div>
<!--1c-->
<div class="os-raise-ib-pset-problem" data-content-id="3e35319d-0d6b-4438-b898-a83eb4302848" data-problem-comparator="integer" data-problem-type="input" data-solution="49">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" >
<li>\(x^2+14x+ \underline{\;\;c\;\;}\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 49 can be added to make the expression a perfect square.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: 49 can be added to make the expression a perfect square. </p>
</div>
</div>
<!--1d-->
<div class="os-raise-ib-pset-problem" data-content-id="9dad8fdb-86ab-4fc5-91d4-2374565cfed6" data-problem-comparator="integer" data-problem-type="input" data-solution="4">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" >
<li>\(x^2−4x+ \underline{\;\;c\;\;}\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 4 can be added to make the expression a perfect square.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: 4 can be added to make the expression a perfect square. </p>
</div>
</div>
<!--1e-->
<div class="os-raise-ib-pset-problem" data-content-id="76a7bb49-df6b-4f07-9e91-fa1907096032" data-problem-comparator="integer" data-problem-type="input" data-solution="144">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>\(x^2+24x+ \underline{\;\;c\;\;}\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 144 can be added to make the expression a perfect square.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: 144 can be added to make the expression a perfect square. </p>
</div>
</div>
<!--2a-->
<div class="os-raise-ib-pset-problem" data-content-id="1a8021f2-29b7-460c-a547-5ada95fee16f" data-problem-comparator="integer" data-problem-type="input" data-solution="-3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<li>If \(x^2−6x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to include the sign.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -3 </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 9.2.2 and 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -3.
</p>
</div>
</div>
<!--2b-->
<div class="os-raise-ib-pset-problem" data-content-id="d27cd74b-c244-438d-95bf-926db14292d5" data-problem-comparator="text" data-problem-type="input" data-solution="+1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" >
<li>If \(x^2+2x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to include the sign.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! +1 </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is +1.
</p>
</div>
</div>
<!--2c-->
<div class="os-raise-ib-pset-problem" data-content-id="34d2148f-1960-4081-8dd9-f3562a759993" data-problem-comparator="text" data-problem-type="input" data-solution="+7">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>If \(x^2+14x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to enter the sign.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! +7</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is +7.
</p>
</div>
</div>
<!--2d-->
<div class="os-raise-ib-pset-problem" data-content-id="0caa8b15-aa41-4a47-895e-6465577e9e88" data-problem-comparator="integer" data-problem-type="input" data-solution="-2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>If \(x^2−4x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to enter the sign.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -2 </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -2.
</p>
</div>
</div>
<!--2e-->
<div class="os-raise-ib-pset-problem" data-content-id="c08b5393-28bf-4e98-96e0-02d1f5945809" data-problem-comparator="text" data-problem-type="input" data-solution="+12">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10">
<li>If \(x^2+24x+c\) is factored to be \((x \_\_\_\_\_)^2\), what is the missing value of the factored form of this expression? Remember to enter the sign.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! +12</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is +12.
</p>
</div>
</div>
<!--3a-->
<div class="os-raise-ib-pset-problem" data-content-id="daff277b-a353-4044-96ee-ad9ea59081f8" data-problem-comparator="integer" data-problem-type="input" data-solution="36">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="11">
<li>Mai is solving the equation \(x^2+12x=13\). She writes:</li>
</ol>
<p>\(x^2+12x=13\)<br>
\((x+6)^2=49\)<br>
\(x=1\) or \(x=-13\)</p>
<p>Jada looks at Mai's work and is confused. She doesn't see how Mai got her answer.</p>
<p>Complete Mai's missing steps by answering questions a–d to help Jada see how Mai solved the equation.</p>
<p>\(x^2+12x=13\)</p>
<p><strong>Step 1 - </strong>\(x^2\;+\;12x\; +\) <u>question a</u> \(=\;13\;+\) <u>question a</u></p>
<p><strong>Step 2 -</strong> \((x+6)^2=49\)</p>
<p><strong>Step 3 - </strong>\(\sqrt{(x+6)^2}=\sqrt{49}\)</p>
<p><strong>Step 4 -</strong> \(x+6= \pm\) <u>question b</u></p>
<p><strong>Step 5 - </strong>\(x+6=\) <u>question b</u></p>
<p><strong>Step 6 -</strong> \(x\;+\;6=\) \(-\)<u>question b</u></p>
<p>\(x=1\) or \(x=-13\)</p>
<p>What is the missing term in Step 1?</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 36</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 36.
</p>
</div>
</div>
<!--3b-->
<div class="os-raise-ib-pset-problem" data-content-id="27ace37f-eb5a-468d-97a5-f15cc4b7470f" data-problem-comparator="integer" data-problem-type="input" data-solution="7">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="12">
<li>What is the missing term in Steps 4, 5, and 6?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 7</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 7.
</p>
</div>
</div>
<!--3c-->
<div class="os-raise-ib-pset-problem" data-content-id="c07dfbfc-4a8b-4a72-91ec-f847b6fad843" data-problem-comparator="integer" data-problem-type="input" data-solution="1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="13">
<li>What is the value of \(x\) in Step 5?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! 1</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 1.
</p>
</div>
</div>
<!--3d-->
<div class="os-raise-ib-pset-problem" data-content-id="c88b63c7-9f5e-4680-8d0e-da4c7639548c" data-problem-comparator="integer" data-problem-type="input" data-solution="-13">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="14">
<li>What is the value of \(x\) in Step 6?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! -13</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -13.
</p>
</div>
</div>
<!--4a-->
<div class="os-raise-ib-pset-problem" data-content-id="a68974c6-171a-48d6-8ba7-8ee9f75aedfa" data-problem-type="multiplechoice" data-retry-limit="5" data-solution="\((x+4)^2=18\)" data-solution-options='["\\((x−7)^2=54\\)", "\\((x+5)^2=12\\)", "\\((x−10)^2=91\\)", "\\((x+4)^2=18\\)", "\\((x+1)^2=1\\)", "\\((x+2)^2=9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="15">
<li>For each equation in questions a–f, choose the equivalent equation with a perfect square on one side.</li>
</ol>
<p>\(x^2+8x=2\) </p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((x+4)^2=18\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \((x+4)^2=18\). </p>
</div>
</div>
<!--4b-->
<div class="os-raise-ib-pset-problem" data-content-id="69d3ec36-966a-47c0-9312-eb11834874ef" data-problem-type="multiplechoice" data-retry-limit="5" data-solution="\((x+5)^2=12\)" data-solution-options='["\\((x−7)^2=54\\) ", "\\((x+5)^2=12\\)", "\\((x−10)^2=91\\)", "\\((x+4)^2=18\\)", "\\((x+1)^2=1\\)", "\\((x+2)^2=9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="16">
<li>\(x^2+10x=-13\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((x+5)^2=12\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \((x+5)^2=12\).
</p>
</div>
</div>
<!--4c-->
<div class="os-raise-ib-pset-problem" data-content-id="e21c7ba8-89c4-44ee-815e-7ba383005675" data-problem-type="multiplechoice" data-retry-limit="5" data-solution="\((x−7)^2=54\)" data-solution-options='["\\((x−7)^2=54\\)", "\\((x+5)^2=12\\)", "\\((x−10)^2=91\\)", "\\((x+4)^2=18\\)", "\\((x+1)^2=1\\)", "\\((x+2)^2=9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="17">
<li>\(x^2−14x=5\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((x−7)^2=54\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \((x−7)^2=54\).
</p>
</div>
</div>
<!--4d-->
<div class="os-raise-ib-pset-problem" data-content-id="38c7644a-a7e8-4d2f-9bd0-dcf06b374b59" data-problem-type="multiplechoice" data-retry-limit="5" data-solution="\((x+1)^2=1\)" data-solution-options='["\\((x−7)^2=54\\)", "\\((x+5)^2=12\\)", "\\((x−10)^2=91\\)", "\\((x+4)^2=18\\)", "\\((x+1)^2=1\\)", "\\((x+2)^2=9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="18">
<li>\(x^2+2x=0\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((x+1)^2=1\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \((x+1)^2=1\).
</p>
</div>
</div>
<!--4e-->
<div class="os-raise-ib-pset-problem" data-content-id="802db0f9-423e-49e8-a434-b7ddff12b747" data-problem-type="multiplechoice" data-retry-limit="5" data-solution="\((x+2)^2=9\)" data-solution-options='["\\((x−7)^2=54\\)", "\\((x+5)^2=12\\)", "\\((x−10)^2=91\\)", "\\((x+4)^2=18\\)", "\\((x+1)^2=1\\)", "\\((x+2)^2=9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="19">
<li>\(x^2+4x−5=0\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((x+2)^2=9\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \((x+2)^2=9\).
</p>
</div>
</div>
<!--4f-->
<div class="os-raise-ib-pset-problem" data-content-id="c20e168d-e932-42c0-a244-a690ebff838c" data-problem-type="multiplechoice" data-retry-limit="5" data-solution="\((x−10)^2=91\)" data-solution-options='["\\((x−7)^2=54\\)", "\\((x+5)^2=12\\)", "\\((x−10)^2=91\\)", "\\((x+4)^2=18\\)", "\\((x+1)^2=1\\)", "\\((x+2)^2=9\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="20">
<li>\(x^2−20x=-9\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((x−10)^2=91\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \((x−10)^2=91\).
</p>
</div>
</div>
<!--5a-->
<div class="os-raise-ib-pset-problem" data-content-id="01ba74f0-4495-49ae-a6f3-b852b9226b0d" data-problem-type="multiselect" data-solution='["\\(x = -1\\)", "\\(x = 7\\)"]' data-solution-options='["\\(x = -1\\)", "\\(x = 5\\)", "\\(x = 2\\)", "\\(x = 7\\)", "\\(x = 6\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="21">
<li>Solve each equation by completing the square, then choose the <strong>two</strong> roots.</li>
</ol>
<p>\(x^2−6x+5=12\)</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(x=-1\) and \(x=7\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are: \(x=-1\) and \(x=7\). </p>
</div>
</div>
<!--5b-->
<div class="os-raise-ib-pset-problem" data-content-id="026ea025-d407-4e51-ad91-854415e91c82" data-problem-type="multiselect" data-solution='["\\(x = -2\\)", "\\(x = 4\\)"]' data-solution-options='["\\(x = 9\\)", "\\(x = -2\\)", "\\(x = 8\\)", "\\(x = 3\\)", "\\(x = 4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="22" >
<li>\(x^2−2x=8\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(x=-2\) and \(x=4\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are: \(x=-2\) and \(x=4\). </p>
</div>
</div>
<!--5c-->
<div class="os-raise-ib-pset-problem" data-content-id="cc4974dc-f7ef-4f80-b674-84e87c241f3c" data-problem-type="multiselect" data-solution='["\\(x = -6\\)", "\\(x = 2\\)"]' data-solution-options='["\\(x = 14\\)", "\\(x = 110\\)", "\\(x = -6\\)", "\\(x = 2\\)", "\\(x = 4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="23">
<li>\(11=x^2+4x−1\)</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(x=-6\) and \(x=2\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are: \(x=-6\) and \(x=2\). </p>
</div>
</div>
<!--6-->
<div class="os-raise-ib-pset-problem" data-content-id="b1e1f763-6ea6-46bd-8a02-8cd017f9bc9b" data-problem-type="multiplechoice" data-retry-limit="4" data-solution="\(x = 9\)" data-solution-options='["\\(x = -21\\)", "\\(x = 9\\)", "\\(x = 39\\)", "\\(x = 78\\)", "\\(x = -39\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="24">
<li>Solve the equation \(x^2−18x+60=-21\) by completing the square.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(x=9\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 9.2.3.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(x=9\).
</p>
</div>
</div>
<!--Do not edit below this line-->
<div class="os-raise-ib-pset-correct-response"> </div>
<div class="os-raise-ib-pset-encourage-response"> </div>
</div>