Graphed in the same standard (x,y) coordinate plane are a circle and a parabola. The circle has radius 3 and center (0,0). The parabola has vertex (-3,-2), has a vertical axis of symmetry, and passes through (-2,-1). The circle and the parabola intersect at how many points?
The correct answer is C.
You can sketch the graphs of the two conics to determine the number of points of intersection. The circle is centered at the origin and has a radius of 3. The vertex of the parabola is (-3,-2), and passes through (-2,-1) so that the parabola turns upward.
The vertex of the parabola is at a distance of √(-32 +22) = √13 coordinate units from the origin and all points on the circle are at a distance of 3 coordinate units from the origin, so the vertex lies outside the circle. Thus, for x < -3, the parabola will not intersect the circle in any points.
For x > 3, the parabola intersects the circle at two distinct points, one on the lower semicircle and one on the upper semicircle.