To find the values of x at the points where y = 4x - x² intersects y = 0, we can set 4x - x² equal to 0 and solve for x.
4x - x² = 0
Factor out x:
x(4 - x) = 0
Therefore, either x = 0 or 4 - x = 0.
If x = 0, then the point where the two curves intersect is (0,0).
If 4 - x = 0, then x = 4 and the point where the two curves intersect is (4,0).
So the values of x at the points where the two curves intersect y = 0 are x = 0 and x = 4.