### Home > PC3 > Chapter 11 > Lesson 11.1.1 > Problem11-9

11-9.

Sketch the graph of $f(x) = −(x + 4)^2(x)(x − 2)^2(x − 3)$ without using a graphing calculator. Do not scale your axes, but be sure to label the important points.

Since $(x + 4)$ is a factor, $x = −4$ is a root, or $x$-intercept. Since the factor is squared, it is actually a double root, so the curve will "bounce" off of the $x$-axis at this intercept.

Sketch a prediction of what the curve looks like without using a graphing calculator. Then, check you work with a graphing calculator, identifying and correcting any mistakes or misconceptions.