CPM Homework Help : PC3 Problem 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.

Step 1:

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

Step 2:

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

Step 3:

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

Step 4:

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

Step 5:

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