Advanced MathVery hardLeading coefficient from a maximum and a point
Advanced Math practice question
The quadratic function f has a maximum value of 12, which occurs at x = −1, and f(1) = 4. What is the value of the leading coefficient of f?
Answer: -2
f(x) = a(x + 1)² + 12. From f(1) = 4: 4a + 12 = 4, so a = −2.
Common wrong answers
- If you answered 2
- 2 has the wrong sign; a maximum needs a negative leading coefficient.
- If you answered -4
- −4 forgets to divide by (1 + 1)² = 4.
- If you answered -8
- −8 is 4a, not a.
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