what is the multi-rule definition for the abs (X^2-2x-8)?

Question

what is the multi-rule definition for the abs (X^2-2x-8)? I know that x=4 and x=-2

I don't know how to come up with multi-rule

 

Answer 1

f(x) = x² -2x -8 is a upward opening parabola with zeros at -2 and 4.

g(x) = |x² - 2x - 8|

For x ≤ -2 the graph of f(x) is above the x-axis, therefore g(x) = x² - 2x - 8.

Likewise for x ≥ 4, the graph f(x) is above the x-axis and g(x) = x² - 2x - 8.

For -2 < x < 4, the graph of f(x) is below the x-axis and , and g(x) = - (x² - 2x - 8).