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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="06f9bcda-dafd-43fb-b8d6-423f240a460c" data-fire-learning-opportunity-event="eventnameY" data-fire-success-event="eventnameX" data-retry-limit="2" data-schema-version="1.0">
<!--q1-->
<div class="os-raise-ib-pset-problem" data-content-id="d21eb73e-0532-407c-8c17-041efa2bbf99" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=x^2-3\)" data-solution-options='["\\(f(x)=x^2+5\\)", "\\(f(x)=x^2-3\\)", "\\(f(x)=x^2\\)", "\\(f(x)=x^2+7\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent">
<li>Choose the quadratic equation that is represented by the graph.</li>
</ol>
<p><img height="166" src="https://k12.openstax.org/contents/raise/resources/bd59d8abb03c9dac56adad4cf8fd4dc0d9bf2f64" width="268"></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph represents \(f(x)=x^2-3\) because the \(y\)-intercept is \((0,-3)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=x^2-3\). The graph represents \(f(x)=x^2-3\) because the \(y\)-intercept is \((0,-3)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward. </p>
</div>
</div>
<!--q2-->
<div class="os-raise-ib-pset-problem" data-content-id="6e27480e-e352-49be-9b6f-44f63467d9a5" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=x^2\)" data-solution-options='["\\(f(x)=x^2+5\\)", "\\(f(x)=x^2-3\\)", "\\(f(x)=x^2\\)", "\\(f(x)=x^2+7\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2">
<li>Choose the quadratic equation that is represented by the graph.</li>
</ol>
<p><img height="166" src="https://k12.openstax.org/contents/raise/resources/adfa84a6542f9a442bd0985740fca99dde05c3fe" width="268"></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph represents \(f(x)=x^2\) because the \(y\)-intercept is \((0,0)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=x^2\). The graph represents \(f(x)=x^2\) because the \(y\)-intercept is \((0,0)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward. </p>
</div>
</div>
<!--q3-->
<div class="os-raise-ib-pset-problem" data-content-id="bfabbcb1-2b5d-4d2e-8a10-460822d6bb93" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=x^2+7\)" data-solution-options='["\\(f(x)=x^2+5\\)", "\\(f(x)=x^2-3\\)", "\\(f(x)=x^2\\)", "\\(f(x)=x^2+7\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="3">
<li>Choose the quadratic equation that is represented by the graph.</li>
</ol>
<p><img height="166" src="https://k12.openstax.org/contents/raise/resources/db8c1a97b5b5d84b10453c8245ae8f09992c8ff9" width="268"></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph represents \(f(x)=x^2+7\) because the \(y\)-intercept is \((0,7)\) and the coefficient of the term \(f(x)=x^2+7\) is a positive 1, so the graph should open upward.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=x^2+7\). The graph represents \(f(x)=x^2+7\) because the \(y\)-intercept is \((0,7)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward. </p>
</div>
</div>
<!--q4-->
<div class="os-raise-ib-pset-problem" data-content-id="ba4aa0c4-e1a5-4e68-874d-f6737f811d7f" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=x^2+5\)" data-solution-options='["\\(f(x)=x^2+5\\)", "\\(f(x)=x^2-3\\)", "\\(f(x)=x^2\\)", "\\(f(x)=x^2+7\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="4">
<li>Choose the quadratic equation that is represented by the graph.</li>
</ol>
<p><img height="166" src="https://k12.openstax.org/contents/raise/resources/cd72afad226904dbabcd17ff4213295c0c300836" width="268"></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph represents \(f(x)=x^2+5\) because the \(y\)-intercept is \((0,5)\) and the coefficient of the term \(f(x)=x^2+5\) is a positive 1, so the graph should open upward.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=x^2+5\). The graph represents \(f(x)=x^2+5\) because the \(y\)-intercept is \((0,5)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward. </p>
</div>
</div>
<!--q5a-->
<div class="os-raise-ib-pset-problem" data-content-id="94861d4e-d17e-4df1-9d09-0e8774e8e2c6" data-problem-type="dropdown" data-retry-limit="1" data-solution="factored form" data-solution-options='["factored form", "standard form"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="5">
<li>The following two equations are equivalent.</li>
</ol>
<p>factored form \(f(x)=(x+2)(x+3)\) <br>
standard form \(f(x)=x^2+5x+6\) </p>
<ol class="os-raise-noindent" type="a">
<li> Which equation helps find the \(x\)-intercepts most efficiently?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The equation written in factored form \(f(x)=(x+2)(x+3)\) because the factors in the expression allow us to see when the expression is 0.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is factored form. The equation written in factored form \(f(x)=(x+2)(x+3) \) because the factors in the expression allow us to see when the expression is 0. </p>
</div>
</div>
<!--5b-->
<div class="os-raise-ib-pset-problem" data-content-id="e021a697-88ee-4d81-a205-df68f64b7376" data-problem-type="dropdown" data-retry-limit="1" data-solution="standard form" data-solution-options='["factored form", "standard form"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> Which equation helps find the \(y\)-intercept most efficiently?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The equation written in standard form \(f(x)=x^2+5x+6\) because the constant term shows us the \(y\)-intercept.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.4.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is standard form. The equation written in standard form \(f(x)=x^2+5x+6\) because the constant term shows us the \(y\)-intercept. </p>
</div>
</div>
<!--6a-->
<div class="os-raise-ib-pset-problem" data-content-id="549853a5-000e-484f-90c1-79f2bae27211" data-problem-type="dropdown" data-retry-limit="1" data-solution="Blue graph (in the middle, opening upward)" data-solution-options='["Green graph (at the bottom, opening downward)", "Blue graph (in the middle, opening upward)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="6">
<li> There are three equations represented on this graph:</li>
</ol>
<p>\(f(x)=x^2\) (black graph, at the top, opening upward)<br>
\(f(x)=x^2-4\)<br>
\(f(x)=-x^2+5\)</p>
<p>Use the graph to answer questions a and b.</p>
<p><img height="192" src="https://k12.openstax.org/contents/raise/resources/f02a214586d1dccfe80f82e0a2c83c4656637b78" width="268"></p>
<ol class="os-raise-noindent" type="a">
<li> Which graph represents the equation \(f(x)=x^2-4\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The blue graph represents \(f(x)=x^2-4\) because the \(y\)-intercept is \((0,-4)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward. </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.12.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p> The correct answer is blue graph (in the middle, opening upward). The blue graph represents \(f(x)=x^2-4\) because the \(y\)-intercept is \((0,-4)\) and the coefficient of the term \(x^2\) is a positive 1, so the graph should open upward. </p>
</div>
</div>
<!--6b-->
<div class="os-raise-ib-pset-problem" data-content-id="10205e3d-e739-41b1-8b9e-175685ffe51b" data-problem-type="dropdown" data-retry-limit="1" data-solution="Green graph (at the bottom, opening downward)" data-solution-options='["Green graph (at the bottom, opening downward)", "Blue graph (in the middle, opening upward)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="2" type="a">
<li> Which graph represents the equation \(f(x)=-x^2+5\)?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The green graph represents \(f(x)=-x^2+5\) because the \(y\)-intercept is \((0,5)\) and the coefficient of the term \(x^2\) is a negative 1, so the graph should open downward. </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.12.2. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is green graph (at the bottom, opening downward). The green graph represents \(f(x)=-x^2+5\) because the \(y\)-intercept is \((0,5)\) and the coefficient of the term \(x^2\) is a negative 1, so the graph should open downward. </p>
</div>
</div>
<!--q7-->
<div class="os-raise-ib-pset-problem" data-content-id="4c5dd1eb-ea08-432e-bf96-40ef5667ac83" data-problem-type="multiselect" data-solution='["\\(f(x)=(x-1)^2\\)", "\\(f(x)=(x+1)(x+2)\\)"]' data-solution-options='["\\(f(x)=x^2+3x-2\\)", "\\(f(x)=x^2-10x\\)", "\\(f(x)=(x-1)^2\\)", "\\(f(x)=5x^2-3x-5\\)", "\\(f(x)=(x+1)(x+2)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="7">
<li> Select two equations whose graphs have a positive \(y\)-intercept.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(x)=(x-1)^2\), \(f(x)=(x+1)(x+2)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.12.2.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are: \(f(x)=(x-1)^2\), \(f(x)=(x+1)(x+2)\). </p>
</div>
</div>
<!--q8-->
<div class="os-raise-ib-pset-problem" data-content-id="5b8cb81c-00b1-4688-b76b-3c1b4ab07a79" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=(x-5)^2\)" data-solution-options='["\\(f(x)=x^2+5\\)", "\\(f(x)=x^2-5\\)", "\\(f(x)=(x+5)^2\\)", "\\(f(x)=(x-5)^2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="8">
<li>Which function represents the graph of \(f(x)=x^2\) shifted 5 units to the right?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The function is \(f(x)=(x-5)^2\) because subtracting 5 from \(x\) shifts the graph to the right 5 units.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=(x-5)^2\). Subtracting 5 from \(x\) shifts the graph to the right 5 units. </p>
</div>
</div>
<!--q9-->
<div class="os-raise-ib-pset-problem" data-content-id="0abd8816-8058-492b-ba67-a32d84901a2c" data-problem-type="multiselect" data-solution='["\\(f(x)=1-x^2\\)", "\\(f(x)=-(x-1)^2\\)", "\\(f(x)=(1-x)(x+2)\\)"]' data-solution-options='["\\(f(x)=(1-x)^2\\)", "\\(f(x)=1-x^2\\)", "\\(f(x)=-(x-1)^2\\)", "\\(f(x)=-1+x^2\\)", "\\(f(x)=(1-x)(x+2)\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="9">
<li>Select three equations whose graphs open downward.</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! \(f(x)=1-x^2\), \(f(x)=-(x-1)^2\), \(f(x)=(1-x)(x+2)\)</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activity 7.12.2 and activity 7.12.5.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answers are: \(f(x)=1-x^2\), \(f(x)=-(x-1)^2\), \(f(x)=(1-x)(x+2)\). </p>
</div>
</div>
<!--q10-->
<div class="os-raise-ib-pset-problem" data-content-id="40de6698-d5bb-4a0c-9372-f40f8f6b0a44" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=(3x)^2\)" data-solution-options='["\\(f(x)=3x^2\\)", "\\(f(x)=(3x)^2\\)", "\\(f(x)=\\frac13x^2\\)", "\\(f(x)={(\\frac13x)}^2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="10">
<li>Which curve is the narrowest?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The function is \(f(x)=(3x)^2\) is the narrowest because multiplying x by a value greater than 1 makes the curve grow faster. \((3x)^2 =9x^2\) , so \(f(x)=(3x)^2\) is the narrowest curve.</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=(3x)^2\). Multiplying \(x^2\) by a value greater than 1 makes the curve narrower. \((3x)^2 =9x^2\) , so \(f(x)=(3x)^2\) is the narrowest curve. </p>
</div>
</div>
<!--q11-->
<div class="os-raise-ib-pset-problem" data-content-id="59bc177a-332c-4bc1-b521-4f21086e378d" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)=-{(x-4)}^2+4\)" data-solution-options='["\\(f(x)={(x-4)}^2+4\\)", "\\(f(x)={(x+4)}^2+4\\)", "\\(f(x)=-{(x-4)}^2+4\\)", "\\(f(x)=-{(x+4)}^2+4\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="11">
<li>Which equation is represented by the graph?</li>
</ol>
<p><img height="192" src="https://k12.openstax.org/contents/raise/resources/fc657952ff3dc0167c3490f2019580516f49e586"></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph represents \(f(x)=-{(x-4)}^2+4\) because the graph is moved 4 units right and 4 units up and the squared term is multiplied by negative 1, so the graph should open downward. </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5.</p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=-{(x-4)}^2+4\). The graph represents \(f(x)=-{(x-4)}^2+4\) because the graph is moved 4 units right and 4 units up and the squared term is multiplied by negative 1, so the graph should open downward. </p>
</div>
</div>
<!--q12-->
<div class="os-raise-ib-pset-problem" data-content-id="46ffb136-295e-46ce-9789-3497e2b34928" data-problem-type="multiplechoice" data-retry-limit="3" data-solution="\(f(x)={(x+2)}^2+3\)" data-solution-options='["\\(f(x)={(x-2)}^2+3\\)", "\\(f(x)={(x-3)}^2+2\\)", "\\(f(x)={(x+2)}^2+3\\)", "\\(f(x)={(x+3)}^2+2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="12">
<li>Which equation is represented by the graph?</li>
</ol>
<p><img alt="Graph on coordinate plane. Horizontal axis by twos from negative 8 to 8. Vertical axis by twos from negative 4 to 8. Graph goes through point 0 comma 7." height="192" src="https://k12.openstax.org/contents/raise/resources/0c9e5c47508f4c799bd5a6d9399b43a536189bb2"></p>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! The graph represents \(f(x)=(x+2)^2+3\) because the graph is moved 2 units left and 3 units up and the squared term is multiplied by positive 1, so the graph should open upward. </p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. Revisit activities 7.12.2–7.12.5. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is: \(f(x)=(x+2)^2+3\). The graph represents \(f(x)=(x+2)^2+3\) because the graph is moved 2 units left and 3 units up and the squared term is multiplied by positive 1, so the graph should open upward. </p>
</div>
</div>
<!--Q#13-->
<div class="os-raise-ib-pset-problem" data-content-id="1ce92a00-0789-432e-9eee-cadf08545987" data-problem-type="multiplechoice" data-solution="\(x+9=52\)" data-solution-options='["Graph d", "Graph a", "Graph c", "Graph d"]'>
<div class="os-raise-ib-pset-problem-content">
<p>For questions 13 - 14, use the following graph. </p>
<p><img src="https://k12.openstax.org/contents/raise/resources/f02a214586d1dccfe80f82e0a2c83c4656637b78" width="300"></p>
<ol class="os-raise-noindent" start="13">
<li>Which of the graphs has been horizontally stretched? </li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! Graph d</p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is Graph d</p>
</div>
</div>
<!--Q#14-->
<div class="os-raise-ib-pset-problem" data-content-id="0a7c4d1b-b296-460c-b1de-e2e27b90f8d1" data-problem-type="multiplechoice" data-solution="\(x+9=52\)" data-solution-options='["\\(f(x) = (x - 2.5)^2\\)", "\\(f(x) = (4x)^2\\)", "\\(f(x) = (x + 2.5)^2\\)", "\\(\\f(x) = (14x)^2\\)"]'>
<div class="os-raise-ib-pset-problem-content">
<ol class="os-raise-noindent" start="14">
<li>Which function most closely represents the equation for graph c?</li>
</ol>
</div>
<div class="os-raise-ib-pset-correct-response">
<p>Correct! <strong></strong></p>
</div>
<div class="os-raise-ib-pset-encourage-response">
<p>Try again. </p>
</div>
<div class="os-raise-ib-pset-attempts-exhausted-response">
<p>The correct answer is <strong></strong></p>
</div>
</div>
<!--END QUESTION.-->
<!--END QUESTION.-->
<!--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>