Question

In the xy-plane, the graph of y=x^2
y=x2and the circle with center (0,2)
and radius 2 have how many points of intersection?

Answer 1

Trying to figure out what you are saying .....

I think you are intersecting y = x^2 and
x^2 + (y-2)^2 = 4

use substitution:
y + (y-2)^2 = 4
y + y^2 - 4y + 4 = 4
y^2 - 3y = 0
y(y - 3) = 0
y = 0 or y = 3

if y = 0, x^2 = 0 ----> x = 0
first intersection point: (0,0) <--- the origin

if y = 3
x^2 = 3
x = ± ?3
2nd point is (?3,3)
3rd point is (-?3,3)

verification: by Wolfram
http://www.wolframalpha.com/input/?i=plot++y+%3D+x%5E2+and+x%5E2+%2B+(y-2)%5E2+%3D+4