# Thread: Graphing functions that have absolute values

1. ## Graphing functions that have absolute values

How do I graph these equations? I know what they're suppose to look like but I don't know what I'm suppose to do (with the absolute values).

y= x^2 - 4|x| + 3

and

y=|x^2 - 4|x| + 3|

2. Originally Posted by mcsquared
How do I graph these equations? I know what they're suppose to look like but I don't know what I'm suppose to do (with the absolute values).

y= x^2 - 4|x| + 3
ok, you seem to know how to graph quadratics, so i won't address that. here is how you deal with the absolute values.

recall the definition of absolute value:

$|x| = \left \{ \begin{array}{lr} x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.$

hence, you have to graph your function piece-wise. note that

$x^2 - 4|x| + 3 = \left \{ \begin{array}{lr} x^2 - 4x + 3 & \mbox{ if } x \ge 0 \\ & \\ x^2 + 4x + 3 & \mbox{ if } x < 0 \end{array} \right.$

so on the interval $[0, \infty)$ you should graph the top function, while on the interval $(-\infty, 0)$ you should graph the bottom function

and
y=|x^2 - 4|x| + 3|
take the graph you drew above, and wherever the graph is negative (below the x-axis) reflect it in the x-axis so that it is positive

3. I think I get it now. Thanks a lot.