Answer
please see image:
Work Step by Step
End behavior:
When $ x\rightarrow-\infty$ , observing just the signs,
we have
$(-)(-)(-)$, so $ P(x)\rightarrow-\infty$
When $ x\rightarrow+\infty$ , observing just the signs,
we have
$(+)(+)(+)$, so $ P(x)\rightarrow+\infty$
Intercepts:
x-intercepts: $x=-2, x=0, x=3.$
y-intercept: $P(0)=0$
Short description of the graph, left to right:
- rises from the bottom left,
- crosses the x-axis at x=-2
- continues rising to a local maximum, turns,
- falling, crosses the x-axis at the origin,
- still falling, continues to a local minimum, turns,
- rising, crosses the x-axis at x=3,
- continues rising indefinitely
