<p>Choose a form using the intercepts or turning point. Substitute another point to find the scale factor.</p>
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<p>Quadratics with the same roots can have different values of \(a\).</p>
<p class="paragraph-header">Choosing a form</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 570px;"><colgroup><col style="width: 31.5789%;"><col style="width: 33.3333%;"><col style="width: 35.0877%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Given on the graph</strong></th><th style="text-align: center; --cell-justify: center"><strong>Start with</strong></th><th style="text-align: center; --cell-justify: center"><strong>Then</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">\(x\)-intercepts \(p\) and \(q\)</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr><tr><td style="text-align: center; --cell-justify: center">Turning point \((h,k)\)</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr></tbody></table></div></div>
<p class="paragraph-header">Example</p>
<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 540px;"><colgroup><col style="width: 38.8889%;"><col style="width: 61.1111%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Given</strong></th><th style="text-align: center; --cell-justify: center"><strong>Working</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Turning point \((2,3)\),<br>passes through \((0,11)\)</td><td class="table-cell--fill-in" style="text-align: center; --cell-justify: center"></td></tr></tbody></table></div></div>
<p>Use a point that gives new information, rather than an intercept or turning point already used.</p>

Choose a form using the intercepts or turning point. Substitute another point to find the scale factor.

Quadratics with the same roots can have different values of \(a\).

Turning point \((2,3)\),
passes through \((0,11)\)

\(\begin{aligned} y&=a(x-2)^2+3 \\ 11&=a(0-2)^2+3 \\ 4a&=8 \\ a&=2 \\ y&=2(x-2)^2+3 \end{aligned}\)

Use a point that gives new information, rather than an intercept or turning point already used.

Given on the graph	Start with	Then
\(x\)-intercepts \(p\) and \(q\)
Turning point \((h,k)\)

Finding a Quadratic Function from a Graph

Finding a Quadratic Function from a Graph