<div class="content-block content-block--columns"><div class="question-columns question-columns--2" data-layout="2"><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765513104039-r3bvtryucqs.png" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div><p style="text-align: center">Minimum Curve</p><p>For the equation $y=\left( x-h \right)\left( x-k \right)$, </p><p>•	the graph opens upwards,</p><p>•	the graph cuts the $x$-axis at $\left( h,0 \right)$ and $\left( k,0 \right)$ and  </p><p>•	the graph is symmetrical about the <strong>vertical</strong> line that passes through the minimum point.</p></div><div class="question-column-divider"></div><div class="question-column" style="flex: 1; align-self: flex-start;"><div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1765513886249-njxzt0qnpu.png" style="max-width: min(300px, 100%); height: auto; display: block;" class="aligncenter custom-width" /></figure></div><p style="text-align: center">Maximum Curve</p><p>For the equation $y=-\left( x-h \right)\left( x-k \right)$,</p><p>•	the graph opens downwards,</p><p>•	the graph cuts the $x$-axis at $\left( h,0 \right)$ and $\left( k,0 \right)$ and  </p><p>•	the graph is symmetrical about the <strong>vertical</strong> line that passes through the maximum point.</p></div></div></div>
<p style="font-size: 1.25rem"><strong>Sketching of graphs of quadratic functions given in the form of</strong></p>
<p style="text-align: center">$y=\pm \left( x-h \right)\left( x-k \right),h&gt;0,k&gt;0$</p>
<p><strong>Step 1:</strong> State the coefficient of ${{x}^{2}}$ to determine if the graph opens upwards or downwards.</p>
<p style="margin-left: 4rem">•	If the coefficient of ${{x}^{2}}&lt;0$, the graph open downwards (maximum curve)</p>
<p style="margin-left: 4rem">•	If the coefficient of ${{x}^{2}}&gt;0$, the graph open upwards (minimum curve)</p>
<p><strong>Step 2:</strong> Obtain the $x$-intercepts by substituting $y=0$ into the equation.  </p>
<p style="margin-left: 4rem">•	Cuts the $x$-axis, $\left( h,0 \right)$ and $\left( k,0 \right)$</p>
<p><strong>Step 3:</strong> Obtain the y-intercept by substituting $x=0$ into the equation. </p>
<p style="margin-left: 4rem">•	Cuts the $y$-axis, $\left( 0,y \right)$</p>
<p><strong>Step 4:</strong> Sketch the graph.</p>

**Sketching of graphs of quadratic functions given in the form of**

$y=\pm \left( x-h \right)\left( x-k \right),h>0,k>0$

**Step 1:** State the coefficient of ${{x}^{2}}$ to determine if the graph opens upwards or downwards.

•	If the coefficient of ${{x}^{2}}<0$, the graph open downwards (maximum curve)

•	If the coefficient of ${{x}^{2}}>0$, the graph open upwards (minimum curve)

**Step 2:** Obtain the $x$-intercepts by substituting $y=0$ into the equation.  

•	Cuts the $x$-axis, $\left( h,0 \right)$ and $\left( k,0 \right)$

**Step 3:** Obtain the y-intercept by substituting $x=0$ into the equation. 

•	Cuts the $y$-axis, $\left( 0,y \right)$

Graphs of the form $y=\pm \left( x-h \right)\left( x-k \right)$

Graphs of the form $y=\pm \left( x-h \right)\left( x-k \right)$

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