Advanced MathMediumWhere a line meets a parabola
Advanced Math practice question
In the xy-plane, the line y = 2x and the parabola y = x² intersect at two points. What is the sum of the x-coordinates of those points?
Answer: 2
Set x² = 2x: x² − 2x = 0 gives x(x − 2) = 0, so x = 0 and x = 2. Their sum is 2.
Common wrong answers
- If you answered 0
- x = 0 is one intersection, but the other is x = 2; the sum is 2.
- If you answered 3
- The intersections are at x = 0 and x = 2, not 1 and 2.
- If you answered 4
- 4 is the y-coordinate at x = 2, not the sum of x-values.
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