The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
Answer
A
The skaters’ paths intersect once, but that point is outside the rink.
B
The skaters’ paths intersect once, and that point is inside the rink.
C
The skaters’ paths intersect twice, but only one of those points is inside the rink.
D
The skaters’ paths intersect twice, and both points are inside the rink.