Answer
From the far left to the far right, the graph
- falls from the upper far left,
- crosses the x axis at $(0.0)$, falling,
- turns and touches the x axis at $(2,0)$ where it
- turns down to fall to the lower far right
Work Step by Step
$P(x)=-2x(x-2)^{2}$
End behavior:
When $ x\rightarrow-\infty$ ,
$-2x$ is positive, $(x-2)^{2}$is positive,
$P(x)$ is positive to the far left.
When $ x\rightarrow+\infty$ ,
$-2x$ is negative, $(x-2)^{2}$ is positive,
$P(x)$ is negative to the far right.
Intercepts:
$ x=0,\quad x-2=0$
x-intercepts:
$x=0$, single (graph crosses x)
$x=2$, double (graph touches x and turns)$.\\\\$
y-intercept: $(0,0)$
From the far left to the far right, the graph
- falls from the upper far left,
- crosses the x axis at $(0.0)$, falling,
- turns and touches the x axis at $(2,0)$ where it
- turns down to fall to the lower far right
