Question

In the xy -plane, the graph of y = x2 and the circle with center (0,1) and radius 3 have how many points of intersection?

Answer 1

Will give medal

Answer 2

You could draw this, or solve algebraically. Which do you prefer?

Answer 3

Or, you could just think about it. The vertex of the parabola is the origin. The origin is inside the circle. The parabola goes upward in both the positive and negative x directions, so it has to hit the circle twice on its way out.