Advanced MathVery hardLeading coefficient from three values
Advanced Math practice question
The function f is defined by f(x) = ax² + bx + c, where a, b and c are constants. If f(0) = 4, f(1) = 5 and f(−1) = 9, what is the value of a?
Answer: 3
f(0) = c = 4. Then f(1) = a + b + 4 = 5 gives a + b = 1, and f(−1) = a − b + 4 = 9 gives a − b = 5. Adding: 2a = 6, so a = 3.
Common wrong answers
- If you answered 1
- 1 is a + b, not a alone.
- If you answered 4
- 4 is c.
- If you answered -2
- −2 is b.
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