Advanced MathHardMinimum from zeros and the y-intercept
Advanced Math practice question
A quadratic function f has zeros at x = 1 and x = 5, and f(0) = 10. What is the minimum value of f?
Answer: -8
f(x) = a(x − 1)(x − 5) with f(0) = 5a = 10, so a = 2. The vertex sits midway at x = 3: f(3) = 2(2)(−2) = −8.
Common wrong answers
- If you answered 3
- 3 is the x-coordinate of the vertex; the minimum VALUE is f(3) = −8.
- If you answered 10
- 10 is f(0), the y-intercept, not the minimum.
- If you answered -4
- With a = 2, f(3) = 2 · (2) · (−2) = −8, twice −4.
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