Advanced MathHardDistance between the intersection points of two parabolas
Advanced Math practice question
In the xy-plane, the graphs of y = x² − 4 and y = −x² + 4 intersect at two points. What is the distance between those points?
Answer: 4
x² − 4 = −x² + 4 gives 2x² = 8, x = ±2, and y = 0 at both. The points (2, 0) and (−2, 0) are 4 apart.
Common wrong answers
- If you answered 0
- 0 is the shared y-coordinate.
- If you answered 2
- 2 is one x-coordinate, half the distance.
- If you answered 8
- 8 is 2x², not a distance.
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