Question

Question #5099c

Answer 1

The absolute value of `x`, indicated with `|x|`, represents the non-negative value of your number regardless of its sign.
For example:
if `x>0` then `|x|=x`: (if `x=3` then `|x|=3`)
otherwise:
if `x<0` then `|x|=-x`: (if `x=-3` then `|x|=-(-3)=3`).

Your function:
`y=f(x)=(x-2)(x+4)=x^2+2x-8` is a quadratic of the type:
`y=ax^2+bx+c`
You must take the absolute value of it, i.e., `|f(x)|`.

Graphically it is represented by a parabola but a parabola in which it is necessary to make POSITIVE all the negative values, so, every time you get a negative you change it into positive.

The shaded area represents the interval of values that were converted from negative to positive:

In the graph below you see the normal function `f(x)` in blue and the one on which the absolute value was applied (`|f(x)|` in red).