Consider the curves y = x² and y = 2|x|. What is the number of points of intersection of the curves?

For y = x² and y = 2|x|, we solve x² = 2|x|. For x ≥ 0: x² = 2x, giving x(x-2) = 0, so x = 0 or x = 2. For x < 0: x² = -2x, giving x(x+2) = 0, so x = 0 or x = -2. The distinct intersection points are (0,0), (2,4), and (-2,4), giving 3 points of intersection.