Advanced MathHardWhere a function is positive
Advanced Math practice question
The function m is defined by m(x) = −(x − 2)² + 9. For which values of x is m(x) > 0?
- A. −1 < x < 5Correct
- B. x < −1 or x > 5
- C. x > 2
- D. All real x
Answer: A. −1 < x < 5
m(x) = 0 when (x − 2)² = 9, i.e. x = −1 or 5. The parabola opens downward, so m is positive between the zeros.
Why the other answers are wrong
- B. x < −1 or x > 5
- Outside the zeros a downward parabola is negative.
- C. x > 2
- x > 2 is only half the interval and extends past x = 5 where m is negative.
- D. All real x
- m(6) = −7, so not all x.
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