Advanced MathHardSecond intersection of a parabola and a line
Advanced Math practice question
In the xy-plane, the parabola y = x² + 1 and the line y = 2x + 1 both pass through the point (0, 1). What is the x-coordinate of the other point they have in common?
Answer: 2
Set equal: x² + 1 = 2x + 1, so x² − 2x = 0 and x(x − 2) = 0. Besides x = 0 (the given point), the graphs meet at x = 2.
Common wrong answers
- If you answered 1
- 1 is the shared y-intercept, not the x-coordinate of the other intersection.
- If you answered 5
- 5 is the y-coordinate of the other intersection (2² + 1 = 5), not its x-coordinate.
- If you answered -2
- −2 has the wrong sign: x(x − 2) = 0 gives x = 2.
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