Hello, joey1!
Sketch the graph of: .$\displaystyle y\:=\:(1+x)^2 (2x)$
Indicate the coordinates of important points clearly.
By inspection, we see that the $\displaystyle x$intercepts are: .$\displaystyle x = \text{}1,\;2$
Since $\displaystyle x=\text{}1$ has multiplicity 2, the graph is tangent to the $\displaystyle x$axis there.
If $\displaystyle x = 0$, then: .$\displaystyle y = 2$ . . . yintercept $\displaystyle (0,2)$
Using calculus, we find that $\displaystyle x = 1$ is a critical value,
. . and that $\displaystyle (1,4)$ is a maximum point.
The graph looks like this: Code:

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

 *
