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|
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:
$\displaystyle |x| = \left \{ \begin{array}{lr} x & \mbox{ if } x \ge 0 \\ & \\ -x & \mbox{ if } x < 0 \end{array} \right.$
hence, you have to graph your function piece-wise. note that
$\displaystyle x^2 - 4|x| + 3 = \left \{ \begin{array}{lr} x^2 - 4x + 3 & \mbox{ if } x \ge 0 \\ & \\ x^2 + 4x + 3 & \mbox{ if } x < 0 \end{array} \right.$
so on the interval $\displaystyle [0, \infty)$ you should graph the top function, while on the interval $\displaystyle (-\infty, 0)$ you should graph the bottom function
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 positiveand
y=|x^2 - 4|x| + 3|