Answer
Refer to the graph below.
Work Step by Step
The $x$-intercepts of the function's graph can be found by equating each factor to zero then solving each equation to obtain:
\begin{align*}
(x-1)^2&=0 &\text{or}& &(x+2)^3=0\\
x-1&=\pm\sqrt0 &\text{or}& &x+2=\sqrt[3]0\\
x-1&=0 &\text{or}& &x+2=0\\
x&=1 \text{ (multiplicity 2)} &\text{or}& &x=-2 \\
\end{align*}
Thus, the $x$-intercepts are $-2 \text{ and } 1$.
The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$:
\begin{align*}
P(0)&=(0-1)^2(0+2)^3\\
&=(-1)^2(2^3)\\
&=1(8)\\
&=8
\end{align*}
Thus, the $y$-intercept is $8$.
Create a table of values to obtain the one below.
Then, plot each ordered pair and connect the points using a smooth curve.
Refer to the graph above.
