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-1)^3=0& &\text{or}& &x-2=0\\
x+1&=\pm\sqrt0 &\text{or}& &x-1=\sqrt[3]{0}& &\text{or}& &x=2\\
x+1&=0 &\text{or}& &x-1=0\\
x&=-1 \text{ (multiplicity 2) }&\text{or}& &x=1& \\
\end{align*}
Thus, the $x$-intercepts are $-1, 1, \text{ and } 2$.
The $y$-intercept of the function can be found by setting $x=0$ then solving for $y$:
\begin{align*}
P(0)&=-(0+1)^2(0-1)^3(0-2)\\
&=-(1^2)(-1)^3(-2)\\
&=-1(-1)(-2)\\
&=-2
\end{align*}
Thus, the $y$-intercept is $2$.
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.
