Advanced MathHardPositive x where a line meets a parabola
Advanced Math practice question
In the xy-plane, the line y = 2x + 1 and the parabola y = x² − 2 intersect at two points. What is the x-coordinate of the intersection point with positive x?
Answer: 3
x² − 2 = 2x + 1 gives x² − 2x − 3 = (x − 3)(x + 1) = 0, so the positive x is 3.
Common wrong answers
- If you answered 1
- 1 solves x² − 2 = 2x + 1 wrongly by inspection; check 1 − 2 ≠ 3.
- If you answered 7
- 7 is the y-coordinate.
- If you answered -1
- −1 is the other intersection.
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