Answer
please see image:
Work Step by Step
Rewrite (factor out $-1 $ from the first factor):
$P(x)=-(x-2)(x+5)$
End behavior:
When $ x\rightarrow-\infty$ , we have -(negative)(negative),
so $ P(x)\rightarrow-\infty$
When $ x\rightarrow+\infty$ , we have -(positive)(positive),
so $ P(x)\rightarrow-\infty$
x-intercepts: $x=-5, x=2. $
y-intercept: $P(0)=-(-2)(5)=+10.$
P(0.1)=9.69,
so the graph falls right after the y-intercept.
Short description, left to right:
- rises from the bottom left,
- crosses the x-axis at -5,
-continues rising to the local maximum,
which is before the y-axis and above y=10,
- at the maximum, turns downward ,
- crosses the y-axis at y=10,
- continues falling, crosses the x-axis at x=2,
- contiues falling indefinitely
