Question

Give an example of an equation that crosses the x-axis at x=3 and x=-8.

This is a problem on my math homework that I’ve been stuck on. Does anyone know how to help?

Answer 1

The *graph of a function* (and not an equation) f(x) crosses the x-axis for any value of x such that f(x) = 0. We call x a root of f(x) in that case.

The simplest function with roots at both x = 3 and x = -8 is

f(x) = (x - 3) (x + 8)

since

f(3) = (3 - 3) (3 + 8) = 0 • 11 = 0

and

f(-8) = (-8 - 3) (-8 + 8) = -11 • 0 = 0