Advanced MathHardQuadratic from its zeros and y-intercept
Advanced Math practice question
A quadratic function f satisfies f(1) = 0, f(7) = 0, and f(0) = 14. What is the value of f(4)?
Answer: -18
With zeros 1 and 7, f(x) = a(x − 1)(x − 7). Then f(0) = 7a = 14, so a = 2. f(4) = 2(3)(−3) = −18.
Common wrong answers
- If you answered 14
- 14 is f(0).
- If you answered 18
- 18 has the wrong sign: (4 − 1)(4 − 7) = −9.
- If you answered -9
- −9 forgets the factor a = 2.
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