Advanced MathVery hardTwo parabolas intersecting
Advanced Math practice question
In the xy-plane, the graphs of y = 2x² − 3 and y = x² + x + 3 intersect at two points. What is the sum of the x-coordinates of the two points?
Answer: 1
Set them equal: 2x² − 3 = x² + x + 3, so x² − x − 6 = 0, which factors as (x − 3)(x + 2) = 0. The x-coordinates are 3 and −2, and their sum is 1.
Common wrong answers
- If you answered 3
- 3 is only one of the two x-coordinates; the other is −2.
- If you answered -1
- −1 has the wrong sign: the roots are 3 and −2, summing to 1.
- If you answered -6
- −6 is the PRODUCT of the roots (the constant term), not their sum.
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