### Home > PC3 > Chapter 4 > Lesson 4.1.1 > Problem4-6

4-6.

Sketch a graph $f(x)=-(x-4)^2(x+5)$. State the degree of the polynomial and the end behavior of the function.

Identify the degree of the polynomial. If you expanded the polynomial, what would the highest power of $x$ be?

Identify the $x$-intercepts. These occur at the $x$-values that make the factors equal to $0$.

Does the curve bounce or cross at each of the $x$-intercepts?

Recall that the negative sign in the front creates a vertical reflection.

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 the $x$-values increase, the $y$-values ______.
As the $x$-values decrease, the $y$-values ______.