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this is the absolute value symbol. What does the directions ask of you?

it means that the y value of the ordered pair is x^2-x and that the answer will be 0 or positive.

for x <0 x^2-x is much better

The sign scheme is (see image).
So for 0 < x < 1 you have:
f(x) = -(x² - x) = -x² + x (because x²-x is negative there)
for x <=0 and for x >=1 you have:
f(x) = x² - x (because x² - x is positive there, so you just remove the |..| )