Quadratic graph explorer


<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 450px;"><colgroup><col style="width: 22.2222%;"><col style="width: 44.4444%;"><col style="width: 33.3333%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"></th><th style="text-align: center; --cell-justify: center"><p><strong>Shape of graph</strong></p></th><th style="text-align: center; --cell-justify: center"><p><strong>Line of symmetry</strong></p></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center"><p>\(a &gt; 0\)</p></td><td style="text-align: center; --cell-justify: center"><div class="graph-block" data-graph-config="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" data-width="150" data-height="100" data-proportional style="width:150px;height:100px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:150px;--graph-aspect:150 / 100;"></div></td><td style="text-align: center; --cell-justify: center"><p>\(x = \frac{p + q}{2}\)</p></td></tr><tr><td style="text-align: center; --cell-justify: center"><p>\(a &lt; 0\)</p></td><td style="text-align: center; --cell-justify: center"><div class="graph-block" data-graph-config="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" data-width="150" data-height="100" data-proportional style="width:150px;height:100px;max-width:100%;display:flow-root;margin:0 auto;--graph-width:150px;--graph-aspect:150 / 100;"></div></td><td style="text-align: center; --cell-justify: center"><p>\(x = \frac{p + q}{2}\)</p></td></tr></tbody></table></div></div>
<p>The turning point of the quadratic function will lie on the line of symmetry.</p>

The turning point of the quadratic function will lie on the line of symmetry.

	Shape of graph	Line of symmetry
\(a > 0\)		\(x = \frac{p + q}{2}\)
\(a < 0\)		\(x = \frac{p + q}{2}\)

Quadratic Functions in the form of \(y=a\left( x-p \right)\left( x-q \right)\)

Quadratic Functions in the form of \(y=a\left( x-p \right)\left( x-q \right)\)