Advanced MathHardCounting integer inputs below a threshold for a quadratic
Advanced Math practice question
The function f is defined by f(x) = (x − 3)² + 1. For how many integer values of x is f(x) < 10?
Answer: 5
(x − 3)² + 1 < 10 → (x − 3)² < 9 → −3 < x − 3 < 3 → 0 < x < 6. The integers are 1, 2, 3, 4, 5: five of them.
Common wrong answers
- If you answered 3
- 3 counts only 2, 3, 4.
- If you answered 7
- 7 counts 0 and 6, where f(x) = 10, which is not less than 10.
- If you answered 9
- 9 is the bound on (x − 3)², not a count.
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