Question

How do you graph `f(x) = (x+5)^2(x+2)(x-1)`?

Answer 1

Below

Explanation:

First, find your x- and y-intercepts
When `y=0`, `x=-5, -2, 1`
When `x=0`, `y=-50`

Notice the `2` in `(x+5)^2` which tells you that at `x=-5`, there is a double root. So what that means is that at `x=-5`, you should draw a shape that "bounces" off the point.

Also when you expand the beginning of your function, you will notice that you start off with `x^4` and the `4` tells you that it is a form of parabola. Therefore, the ends of your function should be pointing in the same direction

Below is the graph
graph{(x+5)^2(x+2)(x-1) [-10, 10, -5, 5]}