Answer
image:
Work Step by Step
Since $(x-1)$ and $(x+2)$ are factors of $P(x)$, then
x-intercepts: $x=1, x=-2$
(both multiplicity 1, the graph crosses over the x-axis).
P(0)=$(-1)(2)=-2$ (y-intercept)
P(0.1)=-1.89, so the graph rises as it crosses the y-axis.
End behavior:
When $ x\rightarrow-\infty$ , both factors are negative so $ P(x)\rightarrow+\infty$
When $ x\rightarrow+\infty$ , both factors are positive so $ P(x)\rightarrow+\infty$
Description of the graph in words, from left to right:
- it falls from the high upper left,
- crosses the x-axis at $x=-2$,
- continues falling to a minimum point (before the origin, below y=-2),
- after reaching the minimum point, turns upward and crosses the y-axis at x=-2,
- continues rising, crosses the x-axis at x=1, and
- continues to rise indefinitely.