<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="stack">
    <name>
      <text>1.2.11 (Solve by completing the square ax^2+bx+c)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Write {@quad@} in completed square form:</p><p>[[input:ans1]] [[validation:ans1]][[feedback:prt1]]</p>

<p>Hence find the solutions to the quadratic {@quad@}. Write your answers as a list, if there is a  repeated root, enter this twice. </p>
<p>[[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We first need to take out the&nbsp;\(x^2\) coefficient as a factor from the&nbsp;\(x^2\) and \(x\) terms:</p><p>\[{@quad@}={@(a*(ev(x^2+b/a*x,simp))+c),simp=false@} \]</p><p>Now working inside the bracket, we complete the square {@(simp:true,x^2+(b/a)*x)@} using the bracket {@(x+b/(2*a))^2@} and compensating by subtracting \(\left({@b/(2*a)@}\right)^2\):</p><p>\[ \begin{align*} {@quad@} &amp;={@(a*(ev(x^2+b/a*x,simp))+c),simp=false@} \\ &amp;={@(a*(ev((x+b/(2*a))^2,simp)-(ev(b/(2*a),simp))^2)+c),simp=false@} \\ &amp;= {@a*ev((x+b/(2*a))^2,simp) -(make_multsgn("cross"),a*(ev(b/(2*a),simp))^2)+c,simp=false@} \\ &amp;= {@(make_multsgn("blank"),ta1)@} \end{align*} \]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
    <penalty>0.1</penalty>
    <hidden>0</hidden>
    <idnumber/>
    <stackversion>
      <text>2022082900</text>
    </stackversion>
    <questionvariables>
      <text>a:rand_range(2,3);
b:a*rand_range(1,3);
c:rand([-1,1,5,-5,7,-7]); /* make this prime so it has no common factor with a */
quad:a*x^2+b*x+c;
ta1:a*(x+b/(2*a))^2+c-a*(b/(2*a))^2;
ta2: solve(quad,x);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@quad=ta1@}, {@ta2@}</text>
    </questionnote>
    <questiondescription format="moodle_auto_format">
      <text/>
    </questiondescription>
    <questionsimplify>1</questionsimplify>
    <assumepositive>0</assumepositive>
    <assumereal>0</assumereal>
    <prtcorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
    </prtcorrect>
    <prtpartiallycorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
    </prtincorrect>
    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
    <multiplicationsign>none</multiplicationsign>
    <sqrtsign>1</sqrtsign>
    <complexno>i</complexno>
    <inversetrig>cos-1</inversetrig>
    <logicsymbol>lang</logicsymbol>
    <matrixparens>[</matrixparens>
    <isbroken>0</isbroken>
    <variantsselectionseed/>
    <input>
      <name>ans1</name>
      <type>algebraic</type>
      <tans>ta1</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
      <insertstars>0</insertstars>
      <syntaxhint/>
      <syntaxattribute>0</syntaxattribute>
      <forbidwords/>
      <allowwords/>
      <forbidfloat>1</forbidfloat>
      <requirelowestterms>0</requirelowestterms>
      <checkanswertype>0</checkanswertype>
      <mustverify>1</mustverify>
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      <options/>
    </input>
    <input>
      <name>ans2</name>
      <type>algebraic</type>
      <tans>ta2</tans>
      <boxsize>15</boxsize>
      <strictsyntax>1</strictsyntax>
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    </input>
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      <value>1.0000000</value>
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        <text/>
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      <node>
        <name>0</name>
        <description/>
        <answertest>CompSquare</answertest>
        <sans>ans1</sans>
        <tans>quad</tans>
        <testoptions>x</testoptions>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
        <truescore>1</truescore>
        <truepenalty/>
        <truenextnode>-1</truenextnode>
        <trueanswernote>prt1-1-T</trueanswernote>
        <truefeedback format="html">
          <text/>
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        <falseanswernote>prt1-1-F</falseanswernote>
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          <text/>
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    </prt>
    <prt>
      <name>prt2</name>
      <value>1.0000000</value>
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      <feedbackvariables>
        <text/>
      </feedbackvariables>
      <node>
        <name>0</name>
        <description/>
        <answertest>AlgEquiv</answertest>
        <sans>setify(ans2)</sans>
        <tans>setify(ta2)</tans>
        <testoptions/>
        <quiet>0</quiet>
        <truescoremode>=</truescoremode>
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          <text/>
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    </prt>
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    <deployedseed>1959709701</deployedseed>
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    <deployedseed>1668280796</deployedseed>
    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt1-1-T</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
    <qtest>
      <testcase>2</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>quad</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
      <expected>
        <name>prt1</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt1-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt2</name>
        <expectedscore>1.0000000</expectedscore>
        <expectedpenalty>0.0000000</expectedpenalty>
        <expectedanswernote>prt2-1-T</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
