# Polynomial (Graph/ Absolute value function)

(CIE 0606/2020/w/11/Q1)
The diagram shows the graph of $y=|p(x)|$, where $p(x)$ is a cubic function. Find the two possible expressions for $p(x)$. [3]

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*********math solution*************
The roots of $p(x)=0$ is $x=-2,x=-1,$ and $x=4.$  Thus

$p(x)=k(x+2)(x+1)(x-4).$ Moreover $|p(0)|=24.$

$\begin{array}{rcl}|k(0+2)(0+1)(0-4)|&=&24\\ -8k&=&\pm 24\\ k&=&\pm 3\end{array}$

Hence $p(x)=\pm 3(x+2)(x+1)(x-4).$
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