Answer
From the far left to the far right, the graph
- falls from $+\infty$, the upper far left,
- crosses the $x$-axis at $(-2,0)$, after which it turns, rising to
- flatten out near $(0,0)$ where it crosses the x-axis, rising,
- turns to touch the x-axis at $(3,0),$
- where it turns to rise to the far right.
Work Step by Step
End behavior:
When $ x\rightarrow-\infty$ , the squared factor is positive, the cubed and linear are negative
$P(x)$ is positive to the far left.
When $ x\rightarrow+\infty$ , all factors are positive,
$P(x)$ is positive to the far right.
Intercepts:
$ x=0,\quad x+2=0,\quad x-3=0$
x-intercepts:
$x=-2$, single (graph crosses x)$.\\\\$
$x= 0,$ triple (graph flattens out at the crossing)$.\\\\$
$x=3$, double (graph touches x and turns)$.\\\\$
y-intercept: $(0,0)$
From the far left to the far right, the graph
- falls from $+\infty$, the upper far left,
- crosses the $x$-axis at $(-2,0)$, after which it turns, rising to
- flatten out near $(0,0)$ where it crosses the x-axis, rising,
- turns to touch the x-axis at $(3,0),$
- where it turns to rise to the far right.
