If x is positive and y negative, the point is in quadrant 4.
If x is negative and y positive, the point is in quadrant 2.
Those are the only two possibilities.
|x| is always zero or positive, whatever the sign of x.
y = |x| is therefore confined to quadrants 1 and 2 which are above the x-axis.
It has no points in quadrants 3 or 4.
The point (0, 0) cannot sensibly be assigned to any quadrant, as it is at the junction of all four quadrants.