Answer
From the far left to the far right, the graph
- rises from $-\infty$ on the far left,
- crosses the x-axis at $(-1,0)$, rising
- turns and falls through $(0,0)$ still falling,
- turns and rises through $(1,0)$ above the x-axis,
- turns back falling through $(2,0),$
- continues falling to the lower far right.
Work Step by Step
Factor out -1 from the last factor and rewrite:
$P(x)=-x(x+1)(x-1)(x-2)$
End behavior:
When $ x\rightarrow-\infty$ , all four factors are negative, a minus is in front: $P(x)$ is negative to the far left.
When $ x\rightarrow+\infty$ , all four factors are positive, a minus is in front: $P(x)$ is negative to the far right.
Intercepts:
$x=0,\quad x+1=0\qquad x-1=0\quad x-2=0$
x-intercepts: at $x=-1, x=0,\ x=1$and $x=2$, all single$.\\\\$
y-intercept: $(0,0)$
From the far left to the far right, the graph
- rises from $-\infty$ on the far left,
- crosses the x-axis at $(-1,0)$, rising
- turns and falls through $(0,0)$ still falling,
- turns and rises through $(1,0)$ above the x-axis,
- turns back falling through $(2,0),$
- continues falling to the lower far right.
