<?xml version="1.0" encoding="UTF-8"?>
<quiz>
  <question type="description">
    <name>
      <text>2.2.8 (Quartics Classification)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h3>Quartic classification</h3>

<p>The forms which can arise in a fully factored quartic are very similar to the ones we have already considered. The table shows the different kinds of term which can appear, and how this affects the graph.</p>

<table style="text-align: center; margin-left:auto; margin-right:auto;" cellpadding="10" border="1" bordercolor="#3a87ad">
<thead>
<tr style="background: #c1ddea">
<th scope="col">Term</th>
<th scope="col">Sketch</th>
<th scope="col">Interpretation</th>
</tr>
</thead>
<tbody>
<tr>
<td>\((x-\alpha)\)</td>
<td><img src="@@PLUGINFILE@@/323_quartic0.svg" alt="Quartic - single term x-alpha" width="130" height="92"></td>
<td>The graph cuts the \(x\)-axis at \(\alpha\)<br></td>
</tr>
<tr>
<td>\((x-\alpha)^2\)</td>
<td><img src="@@PLUGINFILE@@/323_quartic1.svg" alt="Quartic - (x-alpha)^2" width="130" height="92"></td>
<td>The graph touches the&nbsp;\(x\)-axis at \(\alpha\)<br></td>
</tr>
<tr>
<td>\((x-\alpha)^3\)</td>
<td><img src="@@PLUGINFILE@@/323_quartic2.svg" alt="Quartic - (x-alpha)^3" width="130" height="92" class="img-responsive atto_image_button_middle"></td>
<td>The graph crosses the \(x\)-axis at \(\alpha\),<br>and is flat there (called a point of inflection)<br></td>
</tr>
<tr>
<td>\((x-\alpha)^4\)</td>
<td><img src="@@PLUGINFILE@@/323_quartic3.svg" alt="Quartic - (x-alpha)^4" width="130" height="69" class="img-responsive atto_image_button_middle"></td>
<td>The graph touches the&nbsp;\(x\)-axis at \(\alpha\)<br>and is flat there</td>
</tr>
<tr>
<td>One quadratic factor<br>with negative discriminant</td>
<td><img src="@@PLUGINFILE@@/323_quartic4.svg" alt="Quartic - one quadratic with negative discriminant" width="130" height="54" class="img-responsive atto_image_button_middle"></td>
<td>The graph has at most two roots<br></td>
</tr>
<tr>
<td>Two quadratic factors<br>with negative discriminant</td>
<td><img src="@@PLUGINFILE@@/323_quartic5.svg" alt="Quartic - two quadratics with negative discriminant" width="130" height="54" class="img-responsive atto_image_button_middle"></td>
<td>The graph has no roots<br></td>
</tr>
</tbody>
</table>]]></text>
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