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<quiz>
  <question type="stack">
    <name>
      <text>1.2.9 (Solve by completing the square x^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 of {@quad@}. Enter your answers as a list, if there is a repeated root, enter it twice.</p>

<p>[[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Since the \(x\) coefficient is {@bb@} we use \(\frac{b}{2}={@bb/2@}\) in the bracket:</p>
<p>
\[ 
{@(x+bb/2)^2=expand((x+bb/2)^2)@} 
\]</p>
<p>This gives us the correct \(x^2\) and \(x\) terms. Since we want the constant term to be {@cc@} we need to adjust by subtracting {@bb^2/4@} and adding {@cc@}:
</p><p>
\[ 
\begin{align*} 
{@quad@} &amp;= {@(x+bb/2)^2@}-{@(abs(bb)/2)^2@}+{@cc@} \\ &amp;= {@ta1@}. 
\end{align*} 
\]
</p>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2020070100</text>
    </stackversion>
    <questionvariables>
      <text><![CDATA[bb:rand_with_step(-19,-1,2); /*make it odd so that b/2 is not "nice" */
cc:rand_with_prohib(-9,9,[0]);
quad:x^2+bb*x+cc;
ta1:(x+bb/2)^2+cc-(bb/2)^2;
ta2: solve(quad,x);]]></text>
    </questionvariables>
    <specificfeedback format="html">
      <text/>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>{@quad=ta1@}, {@ta2@}</text>
    </questionnote>
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      <text/>
    </questiondescription>
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      <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>
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    <qtest>
      <testcase>1</testcase>
      <description/>
      <testinput>
        <name>ans1</name>
        <value>ta1</value>
      </testinput>
      <testinput>
        <name>ans2</name>
        <value>ta2</value>
      </testinput>
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    <qtest>
      <testcase>2</testcase>
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        <value>quad</value>
      </testinput>
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        <name>ans2</name>
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    </qtest>
  </question>
</quiz>
