Advanced MathHardMaximum value of a downward-opening parabola
Advanced Math practice question
The function f is defined by f(x) = −2(x − 1)² + 7. What is the maximum value of f(x)?
- A. 7Correct
- B. 1
- C. −7
- D. −2
Answer: A. 7
The square (x − 1)² is never negative, and it's multiplied by −2, so −2(x − 1)² is never positive — it's at most 0, when x = 1. So f(x) is at most 0 + 7 = 7, reached at x = 1.
Why the other answers are wrong
- B. 1
- 1 is the x-value WHERE the maximum occurs, not the maximum value itself. The question asks for the largest output, f(1) = 7.
- C. −7
- The +7 is added as-is; nothing flips its sign. The −2 multiplies the square, not the 7.
- D. −2
- −2 is the leading coefficient. It tells you the parabola opens downward (so there IS a maximum), but it isn't the maximum value.
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