Advanced MathMediumSum of the x-intercepts of a parabola in vertex form
Advanced Math practice question
In the xy-plane, the graph of g(x) = −2(x − 1)² + 8 has two x-intercepts. What is the sum of their x-coordinates?
Answer: 2
Set g(x) = 0: (x − 1)² = 4 → x − 1 = ±2 → x = 3 or x = −1. The sum is 2. (By symmetry, the sum is twice the vertex's x-coordinate, 2 × 1.)
Common wrong answers
- If you answered 1
- 1 is the x-coordinate of the vertex, half the sum.
- If you answered 4
- 4 is 3 − (−1), the distance between the intercepts.
- If you answered 8
- 8 is the maximum value of g.
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