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    <name>
      <text>1.3.3 (Graph terminology concave up)</text>
    </name>
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      <text><![CDATA[<p>Consider the following parabola.</p>
<p><img src="@@PLUGINFILE@@/Parabola%20-%20concave%20upwards.png" alt="Parabola - concave upwards" width="332" height="457" /></p>
<br/>
<p>a. Enter the coordinates of the turning point. ([[input:ans11]] [[validation:ans11]],[[input:ans12]] [[validation:ans12]]) [[feedback:prt1]]</p>
<p>b. Is the turning point a minimum or a maximum? [[input:ans2]] [[validation:ans2]][[feedback:prt2]]</p>
<p>c. What is the equation of the axis of symmetry of this parabola? [[input:ans3]] [[validation:ans3]][[feedback:prt3]]</p>
<p>d. By inspecting the graph, what are the roots of the equation represented by this curve? Enter your answer as a list. If there is a repeated root enter this twice. If you believe there are no roots type in <code>none</code>.</p>
<p>[[input:ans4]] [[validation:ans4]][[feedback:prt4]]</p>]]></text>
<file name="Parabola - concave upwards.png" path="/" encoding="base64">[encoded data, 77828 characters]</file>
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    <generalfeedback format="html">
      <text><![CDATA[<p>We can obtain the information that we require by inspecting the graph. We will see later how we can use mathematics in order to obtain this information, however for now looking at the graph, the turning point is the vertex of the graph which is the point \((-3,-4)\). Clearly this is a minimum and the parabola is concave upwards.</p>
<p>The axis of symmetry is the vertical line which passes through the turning point. Therefore it is the line with equation \(x = -3\).</p>
<p>Recall that the roots of the quadratic correspond to the points at which the curve crosses the \(x\)-axis. We can see that on this graph the two roots are therefore 
\[
x = -1 \qquad \mbox{ and } \qquad x = -5.
\]</p>]]></text>
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    <stackversion>
      <text>2020070100</text>
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      <text><![CDATA[ta11: -3;
ta12: -4;

tal2:[[a, false, "maximum"], [b, true, "minimum"]];
ta2:b;

ta3: x = -3;
ta4: solve((x+1)*(x+5),x);]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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    <decimals>.</decimals>
    <scientificnotation>*10</scientificnotation>
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