please help sketch the graph

Hello, joey1!

Quote:

Sketch the graph of: . $y\:=\:(1+x)^2 (2-x)$
Indicate the coordinates of important points clearly.

By inspection, we see that the $x$ -intercepts are: . $x = \text{-}1,\;2$

Since $x=\text{-}1$ has multiplicity 2, the graph is tangent to the $x$ -axis there.

If $x = 0$ , then: . $y = 2$ . . . y-intercept $(0,2)$

Using calculus, we find that $x = 1$ is a critical value,
. . and that $(1,4)$ is a maximum point.

The graph looks like this:

Code:

| * | (1,4) | o * | * * * (0,2)o * * * | - - - - - - o - - + - - + - - o - - (-1,0) | (2,0) | | * |