Points of intersection of a line and a parabola: Find the points of intersection of the graphs of y = 4x - x² and y = 4 - x.

Solving the equations simultaneously, we get

, or

Factoring, we get , or x = 1 and x = 4 are the x coordinates of the points of intersection. We can get the corresponding y coordinates from either of the original equations:

y(1) = 4 - 1 = 3, and y(4) = 4 - 4 = 0. Hence the points are (1,3) and (4,0).

Test Problem: Find the points of intersection of the graphs of y = 3 + 2x - x² and y = x + 1.

a) (1,2) and (2,3)

b) (-1,0) and (2,3)

c) (-1,0) and (-2,-1)

d) (1,2) and (-2,-1)