Q. Determine the minimum value of f(x) = x^2 - 6x + 10. (2019)
Solution
The minimum occurs at x = -b/(2a) = 6/(2*1) = 3. f(3) = 3^2 - 6(3) + 10 = 3.
Correct Answer: B — 3
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Q. Determine the minimum value of the function f(x) = x^2 - 4x + 6. (2020)
Solution
The function is a upward-opening parabola. The minimum occurs at x = -b/(2a) = 4/(2*1) = 2. f(2) = 2^2 - 4(2) + 6 = 2.
Correct Answer: A — 2
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Q. Find the maximum value of f(x) = -3x^2 + 12x - 5. (2020)
Solution
The maximum occurs at x = -b/(2a) = -12/(-6) = 2. f(2) = -3(2^2) + 12(2) - 5 = 7.
Correct Answer: C — 7
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Q. Find the minimum value of f(x) = 4x^2 - 16x + 15. (2023)
Solution
The minimum occurs at x = -b/(2a) = 16/(2*4) = 2. f(2) = 4(2^2) - 16(2) + 15 = 1.
Correct Answer: A — 1
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Q. Find the minimum value of the function f(x) = 3x^2 - 12x + 9. (2022)
Solution
The minimum occurs at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 9 = 3.
Correct Answer: C — 3
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Q. For the function f(x) = -x^2 + 4x + 1, find the maximum value. (2023)
Solution
The maximum occurs at x = -b/(2a) = -4/(-2) = 2. f(2) = -2^2 + 4(2) + 1 = 5.
Correct Answer: B — 5
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Q. What is the maximum value of f(x) = -2x^2 + 10x - 12? (2022)
Solution
The maximum occurs at x = -b/(2a) = -10/(-4) = 2. f(2) = -2(2^2) + 10(2) - 12 = 6.
Correct Answer: C — 6
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Q. What is the minimum value of f(x) = 2x^2 - 8x + 10? (2021)
Solution
The minimum occurs at x = -b/(2a) = 8/(2*2) = 2. f(2) = 2(2^2) - 8(2) + 10 = 2.
Correct Answer: A — 1
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