Advanced MathHardRange of a downward parabola
Advanced Math practice question
The function p is defined by p(x) = −(x − 3)² + 7. Which of the following describes all possible values of p(x)?
- A. p(x) ≤ 7Correct
- B. p(x) ≥ 7
- C. p(x) ≤ 3
- D. All real numbers
Answer: A. p(x) ≤ 7
−(x − 3)² is never positive, so p(x) is at most 7, reached at x = 3.
Why the other answers are wrong
- B. p(x) ≥ 7
- The parabola opens downward, so 7 is the maximum, not the minimum.
- C. p(x) ≤ 3
- 3 is where the maximum occurs, not the maximum value.
- D. All real numbers
- A parabola's values are bounded on one side.
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