Advanced MathHardFinding the leading coefficient from a point
Advanced Math practice question
The function f is defined by f(x) = a(x − 2)² − 8, where a is a constant. If f(0) = 0, what is the value of f(5)?
Answer: 10
f(0) = a(−2)² − 8 = 4a − 8 = 0, so a = 2. Then f(5) = 2(3)² − 8 = 18 − 8 = 10.
Common wrong answers
- If you answered 1
- 1 is f(5) with a = 1: 9 − 8. But f(0) = 0 forces a = 2.
- If you answered 2
- 2 is the value of a, not f(5).
- If you answered 18
- 18 is 2(3)², forgetting to subtract the 8.
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