# Question #5099c

Jan 2, 2015

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 $| x | = - \left(- 3\right) = 3$).

$y = f \left(x\right) = \left(x - 2\right) \left(x + 4\right) = {x}^{2} + 2 x - 8$ is a quadratic of the type:
$y = a {x}^{2} + b x + c$
You must take the absolute value of it, i.e., $| f \left(x\right) |$.

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 $f \left(x\right)$ in blue and the one on which the absolute value was applied ($| f \left(x\right) |$ in red).