Advanced MathHardSum of the x-intercepts from vertex form
Advanced Math practice question
The function f is defined by f(x) = −2(x − 3)² + 8. What is the sum of the x-intercepts of the graph of f in the xy-plane?
Answer: 6
Set f(x) = 0: −2(x − 3)² + 8 = 0, so (x − 3)² = 4 and x − 3 = ±2, giving x = 1 and x = 5. Their sum is 6. (The intercepts are symmetric about the vertex's x-coordinate, 3, so the sum is 2 × 3.)
Common wrong answers
- If you answered 3
- 3 is the x-coordinate of the vertex, halfway between the intercepts; their SUM is twice that.
- If you answered 4
- 4 is (x − 3)², one step before the intercepts.
- If you answered 8
- 8 is the maximum value of f, not a sum of intercepts.
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