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:

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

so on the interval you should graph the top function, while on the interval 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|