Points of intersection of a line and a centered parabola: Find the points of intersection of the graphs of y = x² and y = x + 2.

Solving the equations simultaneously, we get

, or

Factoring, we get , or x = 2 and x = -1 are the x coordinates of the points of intersection. We can get the corresponding y coordinates from either of the original equations:

y(2) = 2+2 = 4, and y(-1) = -1 + 2 = 1. Hence the points are (-1,1) and (2,4).

Test Problem: Find the points of intersection of the graphs of y = x² and y = x + 6.

a) (2,4) and (3,9)

b) (-2,4) and (-3,9)

c) (-2,4) and (3,9)

d) (2,4) and (-3,9)