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PSLE Foundation Mathematics

<p>Let&nbsp;\(f(x) = p(x - q)(x - r)\). Part of the graph of \(f\) is shown below.</p>
<div class="graph-block" data-graph-config="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" data-width="300" data-height="200" style="width:300px;height:200px;max-width:100%;display:block;margin:0 auto;"></div>
<p>The graph passes through the points \( (-2,0), (0, -4) \) and \( (4, 0) \).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down the value of \(q\) and \(r\).<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Write down the <strong>equation</strong> of the axis of symmetry.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the value of \(p\).<span class="inline-marks">[3]</span></div></li></ol>

Let \(f(x) = p(x - q)(x - r)\). Part of the graph of \(f\) is shown below.

The graph passes through the points \( (-2,0), (0, -4) \) and \( (4, 0) \).

Quadratic Graphs and Applications

Functions

Quadratic Functions, Equations and Inequalities

<p>Let&nbsp;\(f(x) = 8x - 2x^2\). Part of the graph of \(f\) is shown below.</p>
<div class="graph-block" data-graph-config="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" data-width="200" data-height="250" style="width:200px;height:250px;max-width:100%;display:block;margin:0 auto;"></div>
<ol class="abc-list"><li><div class="list-item-paragraph">Find the \(x\)-intercepts of the graph.<span class="inline-marks">[4]</span></div></li><li><ol class="i-list"><li><div class="list-item-paragraph">Write down the equation of the axis of symmetry.</div></li><li><div class="list-item-paragraph">Find the \(y\)-coordinate of the vertex.<span class="inline-marks">[3]</span></div></li></ol></li></ol>

Let \(f(x) = 8x - 2x^2\). Part of the graph of \(f\) is shown below.

Solving Quadratic Equations

<p>The diagram below shows the graph of \(y = x^2 - x - 12\).</p>
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1776140313968-zhxc4w63y9.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzYxNDAzMTM5Njgtemh4YzR3NjN5OS5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkyODY3ODQyLCJleHAiOjE3OTI4NjgxNDJ9.tj9Gxq3kSddfm4z1lDv1Sw9KzwyzsX3rCzPTEVaHH-Q" style="max-width: min(250px, 100%); height: auto; display: block;" alt="Graph of a parabola with intercepts A, B, and C" class="aligncenter custom-width" /></figure></div>
<ol class="abc-list"><li><div class="list-item-paragraph">The graph cuts the \(x\)-axis at \(B\) and \(C\). Find the coordinates of \(B\) and \(C\).</div><div class="list-item-paragraph" style="text-align: right">Answer \(B\) (.................... , ....................) <span class="inline-marks">[1]</span></div><div class="list-item-paragraph" style="text-align: right">Answer \(C\) (.................... , ....................)<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Find the gradient of line \(AC\).</div><div class="list-item-paragraph" style="text-align: right">Answer ....................................................<span class="inline-marks">[2]</span></div></li><li><div class="list-item-paragraph">Find the equation of the line of symmetry.</div><div class="list-item-paragraph" style="text-align: right">Answer ....................................................<span class="inline-marks">[1]</span></div></li></ol>

The diagram below shows the graph of \(y = x^2 - x - 12\).

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