CPM Homework Help : PC3 Problem 4-75

Sketch a graph of the polynomial function $p(x)=\frac{1}{4}(x-2)^2(x+2)^3$ . State the intercepts and end behavior.

Hint:

Your curve should have a double root at $x=2$ and a triple root at $x=−2$ .

More Help:

Determine the $y$ -intercept by letting $x=0$ .

Step:

Do not use a calculator! Sketch a prediction of what you think the curve looks like.
Then, use a graphing calculator to check your prediction. Correct any errors you might have made.
Remember that making mistakes and identifying and correcting them is how you build brain cells.

End Behavior:

As $x→∞$ , $y→$ ______.
As $x→−∞$ , $y→$ ______.