### Home > PC3 > Chapter 4 > Lesson 4.2.2 > Problem4-75

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.

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

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

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.

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