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11d31e42-e3f2-4bb8-bc37-1e5be17b98bc.html
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<h4>Activity</h4>
<ol class="os-raise-noindent">
<li>Use the table with different values of \(x\) to answer questions a–g for the values of \(x^2+10\). (You may
also use a spreadsheet tool, if available.)</li>
</ol>
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(x^2+10\) </th>
<td> a. ____ </td>
<td> b. ____ </td>
<td> c. ____ </td>
<td> d. ____ </td>
<td> e. ____ </td>
<td> f. ____ </td>
<td> g. ____ </td>
</tr>
</tbody>
</table>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="29c25dcc-9614-4366-931b-cff6cecf2623" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="56da4227-4773-4148-ad83-e42e2702a677" data-problem-comparator="float" data-problem-type="input" data-solution="19">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" type="a">
<li> When \(x=-3\) and \(x^2=9\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-3)^2+10=9+10=19\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 19. \((-3)^2+10=9+10=19\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="da7dc977-a70d-460f-8c68-b85042fe7f9b" data-problem-comparator="float" data-problem-type="input" data-solution="14">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> When \(x=-2\) and \(x^2=4\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-2)^2+10=4+10=14\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 14. \((-2)^2+10=4+10=14\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="5ecbe22e-6069-44b9-aa7d-9ee9a27d0244" data-problem-comparator="float" data-problem-type="input" data-solution="11">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="a">
<li> When \(x=-1\) and \(x^2=1\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-1)^2+10=1+10=11\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 11. \((-1)^2+10=1+10=11\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1d-->
<div class="os-raise-ib-pset-problem" data-content-id="e52fa14f-0bad-44e3-a59d-807f4583fc09" data-problem-comparator="float" data-problem-type="input" data-solution="10">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="a">
<li> When \(x=0\) and \(x^2=0\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((0)^2+10=0+10=10\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 10. \((0)^2+10=0+10=10\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1e-->
<div class="os-raise-ib-pset-problem" data-content-id="b634d6bc-9e5d-48cc-920b-2d8885844aec" data-problem-comparator="float" data-problem-type="input" data-solution="11">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="a">
<li> When \(x=1\) and \(x^2=1\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((1)^2+10=1+10=11\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 11. \((1)^2+10=1+10=11\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1f-->
<div class="os-raise-ib-pset-problem" data-content-id="ee69e6ea-32ff-4701-9748-be0dd653d934" data-problem-comparator="float" data-problem-type="input" data-solution="14">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="a">
<li> When \(x=2\) and \(x^2=4\), what is value of \(x^2+10\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((2)^2+10=4+10=14\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 14. \((2)^2+10=4+10=14\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1g-->
<div class="os-raise-ib-pset-problem" data-content-id="b0b9ca01-0aaf-4afc-8fda-f32204c05a8d" data-problem-comparator="float" data-problem-type="input" data-solution="19">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="a">
<li> When \(x=3\) and \(x^2=9\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((3)^2+10=9+10=19\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 19. \((3)^2+10=9+10=19\)</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>
<ol class="os-raise-noindent" start="2">
<li>Use the table with different values of \(x\) to answer questions a–g for the values of \(x^2-3\). (You may
also use a spreadsheet tool, if available.)</li>
</ol>
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(x^2-3\) </th>
<td> a. ____ </td>
<td> b. ____ </td>
<td> c. ____ </td>
<td> d. ____ </td>
<td> e. ____ </td>
<td> f. ____ </td>
<td> g. ____ </td>
</tr>
</tbody>
</table>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="847e7f11-312b-4f7e-ad9c-83f1fd55b405" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="414a4c79-f8ca-4d84-bdb0-3799b2d22150" data-problem-comparator="float" data-problem-type="input" data-solution="6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" type="a">
<li> When \(x=-3\) and \(x^2=9\), what is value of \(x^2-3\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-3)^2-3=9-3=6\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 6. \((-3)^2-3=9-3=6\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="f903c1c9-b5cf-482c-a4ca-22c9fa11ad99" data-problem-comparator="float" data-problem-type="input" data-solution="1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> When \(x=-2\) and \(x^2=4\), what is value of \(x^2-3\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-2)^2-3=4-3=1\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 1. \((-2)^2-3=4-3=1\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="9da988cd-6c24-4c40-b6ec-1f4ee1a64054" data-problem-comparator="float" data-problem-type="input" data-solution="-2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="a">
<li> When \(x=-1\) and \(x^2=1\), what is value of \(x^2-3\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((-1)^2-3=1-3=-2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -2. \((-1)^2-3=1-3=-2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1d-->
<div class="os-raise-ib-pset-problem" data-content-id="e7496405-bc12-4bc9-adcf-b73b9aec4f83" data-problem-comparator="float" data-problem-type="input" data-solution="-3">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="a">
<li> When \(x=0\) and \(x^2=0\), what is value of \(x^2-3\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((0)^2-3=0-3=-3\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -3. \((0)^2-3=0-3=-3\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1e-->
<div class="os-raise-ib-pset-problem" data-content-id="a09868fb-17d3-46d0-b856-6287faee4786" data-problem-comparator="float" data-problem-type="input" data-solution="-2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="a">
<li> When \(x=1\) and \(x^2=1\), what is value of \(x^2-3\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2. (1)2-3=1-3=-2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -2. \(-2. (1)2-3=1-3=-2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1f-->
<div class="os-raise-ib-pset-problem" data-content-id="29189482-f312-4e41-9f3b-fbf3c52bb5ef" data-problem-comparator="float" data-problem-type="input" data-solution="1">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="a">
<li> When \(x=2\) and \(x^2=4\), what is value of \(x^2-3\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((2)^2-3=4-3=1\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 1. \((2)^2-3=4-3=1\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1g-->
<div class="os-raise-ib-pset-problem" data-content-id="36a5a0df-8eed-4890-974e-47533bc33e7c" data-problem-comparator="float" data-problem-type="input" data-solution="6">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="a">
<li> When \(x=3\) and \(x^2=9\), what is value of \(x^2+10\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \((3)^2-3=9-3=6\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 6. \((3)^2-3=9-3=6\)</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>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal1a" data-schema-version="1.0">
<div class="os-raise-ib-cta-content"> </div>
<div class="os-raise-ib-cta-prompt">
<p>Select the <strong>solution</strong> button to see the solutions to questions 1 and 2 organized into a table.</p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal1a">
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(x^2+10\) </th>
<td> 19 </td>
<td> 14 </td>
<td> 11 </td>
<td> 10 </td>
<td> 11 </td>
<td> 14 </td>
<td> 19 </td>
</tr>
<tr>
<th scope="row"> \(x^2-3\) </th>
<td> 6 </td>
<td> 1 </td>
<td> -2 </td>
<td> -3 </td>
<td> -2 </td>
<td> 1 </td>
<td> 6 </td>
</tr>
</tbody>
</table>
<br>
</div>
<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">
<ol class="os-raise-noindent" start="3">
<li>In the earlier activity “Transformations with Quadratic Functions,” you observed the effects on
the graph of adding or subtracting a constant term from \(x^2\). Study the values in the table created from
questions 1 and 2 in this activity. Use these values to explain why the graphs in the earlier activity changed
the way they did when a constant term is added or subtracted.</li>
</ol>
</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>Compare your answer:</p>
<p>All values in the third row are 10 more than those in the second row, and all values in the last row are 3 less
than those in the second row. This suggests that all the points that represent \(x^2+10\) are 10 units higher on the
graph than those for \(x^2\), and all the points that represent \(x^2-3\) are 3 units lower than those for \(x^2\),
which explains why the graphs move up or down when a constant term is added or subtracted.</p>
</div>
<ol class="os-raise-noindent" start="4">
<li>Use the table with different values of \(x\) to answer questions a–g for the values of \(2x^2\). (You may
also use a spreadsheet tool, if available.)</li>
</ol>
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(2x^2\) </th>
<td> a. _____ </td>
<td> b. _____ </td>
<td> c. _____ </td>
<td> d. _____ </td>
<td> e. _____ </td>
<td> f. _____ </td>
<td> g. _____ </td>
</tr>
</tbody>
</table>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="5c5b9689-768d-4dbe-b36d-2b656b6e72d4" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="741e766d-8bc5-47dd-9de6-745f6ed37a69" data-problem-comparator="float" data-problem-type="input" data-solution="18">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" type="a">
<li> When \(x=-3\) and \(x^2=9\), what is value of \(2x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(-3)^2=2 \cdot 9=18\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 18. \(2(-3)^2=2 \cdot 9=18\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="f6d75941-6000-4943-a2bb-c1fa0c310e0b" data-problem-comparator="float" data-problem-type="input" data-solution="8">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> When \(x=-2\) and \(x^2=4\), what is value of \(2x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(-2)^2=2 \cdot 4=8\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 8. \(2(-2)^2=2 \cdot 4=8\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="7a7b18dd-3cf5-4867-af32-5236de55f86d" data-problem-comparator="float" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="a">
<li> When \(x=-1\) and \(x^2=1\), what is value of \(2x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(-1)2=2 \cdot 1=2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 2. \(2(-1)2=2 \cdot 1=2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1d-->
<div class="os-raise-ib-pset-problem" data-content-id="ed8cb8ce-10ca-4b3c-8733-b9355270955f" data-problem-comparator="float" data-problem-type="input" data-solution="0">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="a">
<li> When \(x=0\) and \(x^2=0\), what is value of \(2x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(0)^2=2 \cdot 0=0\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 0. \(2(0)^2=2 \cdot 0=0\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1e-->
<div class="os-raise-ib-pset-problem" data-content-id="16af383e-a948-4a67-90c8-6921a04c6dc4" data-problem-comparator="float" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="a">
<li> When \(x=1\) and \(x^2=1\), what is value of \(2x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(1)^2=2 \cdot 1=2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 2. \(2(1)^2=2 \cdot 1=2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1f-->
<div class="os-raise-ib-pset-problem" data-content-id="55dbbb41-7edf-4c57-8ee1-18495cce6d54" data-problem-comparator="float" data-problem-type="input" data-solution="8">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="a">
<li> When \(x=2\) and \(x^2=4\), what is value of \(2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(2)^2=2 \cdot 4=8\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 8. \(2(2)^2=2 \cdot 4=8\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1g-->
<div class="os-raise-ib-pset-problem" data-content-id="6a173281-6359-4277-9e56-378b2c27cddd" data-problem-comparator="float" data-problem-type="input" data-solution="18">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="a">
<li> When \(x=3\) and \(x^2=9\), what is value of \(2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(2(3)^2=2 \cdot 9=18\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 18. \(2(3)^2=2 \cdot 9=18\)</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>
<ol class="os-raise-noindent" start="5">
<li>Use the table with different values of \(x\) to answer questions a–g for the values of \(\frac{1}{2}x^2\).
(You may also use a spreadsheet tool, if available.)</li>
</ol>
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(\frac{1}{2}x^2\) </th>
<td> a. _____ </td>
<td> b. _____ </td>
<td> c. _____ </td>
<td> d. _____ </td>
<td> e. _____ </td>
<td> f. _____ </td>
<td> g. _____ </td>
</tr>
</tbody>
</table>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="e61cfef3-73d7-4929-9705-bfefb0eec391" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="12964d60-9f81-4912-977d-ded91307039c" data-problem-comparator="float" data-problem-type="input" data-solution="4.5">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" type="a">
<li> When \(x=-3\) and \(x^2=9\), what is value of \(\frac{1}{2}x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(-3)^2=\frac{1}{2} \cdot 9=\frac{9}{2}=4\frac{1}{2}=4.5\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 4.5. \(\frac{1}{2}(-3)^2=\frac{1}{2} \cdot 9=\frac{9}{2}=4\frac{1}{2}=4.5\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="e3e9bc8c-3d92-4254-833a-c959d25c753d" data-problem-comparator="float" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> When \(x=-2\) and \(x^2=4\), what is value of \(\frac{1}{2}x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(-2)^2=\frac{1}{2} \cdot 4=\frac{4}{2}=2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 2. \(\frac{1}{2}(-2)^2=\frac{1}{2} \cdot 4=\frac{4}{2}=2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="aebd7c88-b1e9-429d-8c26-0be943403732" data-problem-comparator="float" data-problem-type="input" data-solution="0.5">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="a">
<li> When \(x=-1\) and \(x^2=1\), what is value of \(\frac{1}{2}x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(-1)^2=\frac{1}{2} \cdot 1=\frac{1}{2}=0.5\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 0.5. \(\frac{1}{2}(-1)^2=\frac{1}{2} \cdot 1=\frac{1}{2}=0.5\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1d-->
<div class="os-raise-ib-pset-problem" data-content-id="19f7e9d6-11eb-42e9-8bc4-663b58043a4b" data-problem-comparator="float" data-problem-type="input" data-solution="0">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="a">
<li> When \(x=0\) and \(x^2=0\), what is value of \(\frac{1}{2}x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(0)^2=\frac{1}{2} \cdot 0=0\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 0. \(\frac{1}{2}(0)^2=\frac{1}{2} \cdot 0=0\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1e-->
<div class="os-raise-ib-pset-problem" data-content-id="34793db7-7916-4c17-8e7d-5c350ef56e33" data-problem-comparator="float" data-problem-type="input" data-solution="0.5">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="a">
<li> When \(x=1\) and \(x^2=1\), what is value of \(\frac{1}{2}x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(1)^2=\frac{1}{2} \cdot 1=\frac{1}{2}=0.5\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 0.5. \(\frac{1}{2}(1)^2=\frac{1}{2} \cdot 1=\frac{1}{2}=0.5\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1f-->
<div class="os-raise-ib-pset-problem" data-content-id="a9602fee-e393-45f9-b26b-51f46f3fdc41" data-problem-comparator="float" data-problem-type="input" data-solution="2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="a">
<li> When \(x=2\) and \(x^2=4\), what is value of \(\frac{1}{2}x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(2)2=\frac{1}{2} \cdot 4=\frac{4}{2}=2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 2. \(\frac{1}{2}(2)2=\frac{1}{2} \cdot 4=\frac{4}{2}=2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1g-->
<div class="os-raise-ib-pset-problem" data-content-id="a99a5c26-6a0d-4e72-82ed-ec405c1f1e47" data-problem-comparator="float" data-problem-type="input" data-solution="4.5">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="a">
<li> When \(x=3\) and \(x^2=9\), what is value of \(\frac{1}{2}x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(\frac{1}{2}(3)^2=\frac{1}{2} \cdot 9=\frac{9}{2}=4\frac{1}{2}=4.5\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 4.5. \(\frac{1}{2}(3)^2=\frac{1}{2} \cdot 9=\frac{9}{2}=4\frac{1}{2}=4.5\)</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>
<ol class="os-raise-noindent" start="6">
<li>Use the table with different values of \(x\) to answer questions a–g for the values of \(-2x^2\) . (You may
also use a spreadsheet tool, if available.) </li>
</ol>
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(-2x^2\) </th>
<td> a. _____ </td>
<td> b. _____ </td>
<td> c. _____ </td>
<td> d. _____ </td>
<td> e. _____ </td>
<td> f. _____ </td>
<td> g. _____ </td>
</tr>
</tbody>
</table>
<br>
<div class="os-raise-ib-pset" data-button-text="Check" data-content-id="0abb16d7-c01d-4e55-8d3d-1eee7e2fa4b8" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="0" data-schema-version="1.0">
<!--Q1a-->
<div class="os-raise-ib-pset-problem" data-content-id="1ef18c42-7b66-4440-b804-f22f26238680" data-problem-comparator="float" data-problem-type="input" data-solution="-18">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" type="a">
<li> When \(x=-3\) and \(x^2=9\), what is value of \(-2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(-3)^2=-2 \cdot 9=-18\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -18. \(-2(-3)^2=-2 \cdot 9=-18\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1b-->
<div class="os-raise-ib-pset-problem" data-content-id="49a47e47-fe91-40f5-8b9c-f7e12aa93cb7" data-problem-comparator="float" data-problem-type="input" data-solution="-8">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> When \(x=-2\) and \(x^2=4\), what is value of \(-2x^2\)?</li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(-2)^2=-2 \cdot 4=-8\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -8. \(-2(-2)^2=-2 \cdot 4=-8\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1c-->
<div class="os-raise-ib-pset-problem" data-content-id="de9fc74b-58ce-4763-bb13-43ffae05b658" data-problem-comparator="float" data-problem-type="input" data-solution="-2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3" type="a">
<li> When \(x=-1\) and \(x^2=1\), what is value of \(-2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(-1)^2=-2 \cdot 1=-2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -2. \(-2(-1)^2=-2 \cdot 1=-2\)</p>
</div>
</div>
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<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4" type="a">
<li> When \(x=0\) and \(x^2=0\), what is value of \(-2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(0)^2=-2 \cdot 0=0\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is 0. \(-2(0)^2=-2 \cdot 0=0\)</p>
</div>
</div>
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<div class="os-raise-ib-pset-problem" data-content-id="7cdbb75f-e4db-4503-9a20-d0cd22ce4d2f" data-problem-comparator="float" data-problem-type="input" data-solution="-2">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5" type="a">
<li> When \(x=1\) and \(x^2=1\), what is value of \(-2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(1)^2=-2 \cdot 1=-2\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -2. \(-2(1)^2=-2 \cdot 1=-2\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1f-->
<div class="os-raise-ib-pset-problem" data-content-id="2bdcc76e-34cf-47ad-a401-e3883a0314a3" data-problem-comparator="float" data-problem-type="input" data-solution="-8">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6" type="a">
<li> When \(x=2\) and \(x^2=4\), what is value of \(-2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(2)^2=-2 \cdot 4=-8\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -8. \(-2(2)^2=-2 \cdot 4=-8\)</p>
</div>
</div>
<!--END QUESTION.-->
<!--Q1g-->
<div class="os-raise-ib-pset-problem" data-content-id="246cb693-cf66-408c-b773-b892056f5dcf" data-problem-comparator="float" data-problem-type="input" data-solution="-18">
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7" type="a">
<li> When \(x=3\) and \(x^2=9\), what is value of \(-2x^2\)? </li>
</ol>
<p>Enter your answer here:</p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(-2(3)^2=-2 \cdot 9=-18\)</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is -18.\(-2(3)^2=-2 \cdot 9=-18\)</p>
</div>
</div>
<!--END QUESTION.-->
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</div>
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<br>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2a" data-schema-version="1.0">
<div class="os-raise-ib-cta-content"> </div>
<div class="os-raise-ib-cta-prompt">
<p>Select the <strong>solution</strong> button to see the solutions to questions 4–6 organized into a table. </p>
</div>
</div>
<div class="os-raise-ib-content" data-schema-version="1.0" data-wait-for-event="Reveal2a">
<table class="os-raise-horizontaltable">
<thead>
</thead>
<tbody>
<tr>
<th scope="row"> \(x\) </th>
<td> -3 </td>
<td> -2 </td>
<td> -1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 2 </td>
<td> 3 </td>
</tr>
<tr>
<th scope="row"> \(x^2\) </th>
<td> 9 </td>
<td> 4 </td>
<td> 1 </td>
<td> 0 </td>
<td> 1 </td>
<td> 4 </td>
<td> 9 </td>
</tr>
<tr>
<th scope="row"> \(2x^2\) </th>
<td> 18 </td>
<td> 8 </td>
<td> 2 </td>
<td> 0 </td>
<td> 2 </td>
<td> 8 </td>
<td> 18 </td>
</tr>
<tr>
<th scope="row"> \(\frac{1}{2}x^2\) </th>
<td> \(4\frac{1}{2}=4.5\) </td>
<td> 2 </td>
<td> \(\frac{1}{2}=0.5\) </td>
<td> 0 </td>
<td> \(\frac{1}{2}=0.5\) </td>
<td> 2 </td>
<td> \(4\frac{1}{2}=4.5\) </td>
</tr>
<tr>
<th scope="row"> \(-2x^2\) </th>
<td> -18 </td>
<td> -8 </td>
<td> -2 </td>
<td> 0 </td>
<td> -2 </td>
<td> -8 </td>
<td> -18 </td>
</tr>
</tbody>
</table>
<br>
</div>
<div class="os-raise-ib-cta" data-button-text="Solution" data-fire-event="Reveal2b" data-schema-version="1.0">
<div class="os-raise-ib-cta-content">
<ol class="os-raise-noindent" start="7">
<li>In the earlier activity “Transformations with Quadratic Functions,” you observed the effects on
the graph of multiplying \(x^2\) by different coefficients. Study the values in the table created from questions
1 and 2 in this activity. Use these values to explain why the graphs in the earlier activity changed the way
they did when \(x^2\) is multiplied by a number greater than 1, by a negative number less than or equal to -1,
and by numbers between -1 and 1.</li>
</ol>
</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="Reveal2b">
<p>Compare your answer:</p>
<p>When we multiply \(x^2\) by the positive coefficient 2, all the output values double. For any input value \(x\) ,
the output value of \(2x^2\) is twice as large as that of \(x^2\). So, the width of the graph becomes narrower
because it grows faster. When we multiply \(x^2\) by a number between 0 and 1, the output values become smaller, so
the graph becomes wider or vertically compressed. When we multiply by a negative number, all the positive values
become negative, which reflects the direction of the opening of the graph from opening up to opening down.</p>
</div>
<h4>Video: Understanding the Behaviors of a Graph in Relation to Its Quadratic Expression</h4>
<p>Watch the following video to learn more about the behaviors of a graph in relation to its quadratic expression.</p>
<div class="os-raise-d-flex-nowrap os-raise-justify-content-center">
<div class="os-raise-video-container"><video controls="true" crossorigin="anonymous">
<source src="https://k12.openstax.org/contents/raise/resources/51a23e0458b71ce1bf5fda19ecbeb56d402c37cf">
<track default="true" kind="captions" label="On" src="https://k12.openstax.org/contents/raise/resources/6490961d643c5011adcc5ed8c591599bb1aaec5e" srclang="en_us">
https://k12.openstax.org/contents/raise/resources/51a23e0458b71ce1bf5fda19ecbeb56d402c37cf
</video></div>
</div>