Advanced MathHardWhere a quadratic exceeds its constant term
Advanced Math practice question
The function h is defined by h(x) = −x² + 4x + 12. For which values of x is h(x) greater than 12?
- A. 0 < x < 4Correct
- B. x > 4
- C. x < 0 or x > 4
- D. −4 < x < 0
Answer: A. 0 < x < 4
h(x) > 12 means −x² + 4x > 0, or x(4 − x) > 0, which holds exactly when 0 < x < 4.
Why the other answers are wrong
- B. x > 4
- For x > 4, x(4 − x) is negative, so h(x) < 12.
- C. x < 0 or x > 4
- Those are the values where h(x) is less than 12.
- D. −4 < x < 0
- For −4 < x < 0, x(4 − x) is negative.
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