Sketch the graph of $y=(1+x)^2 (2-x)$

Indicate the coordinates of important points clearly.

2. Hello, joey1!

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)
|
|            *
|