Question:
A quadratic function \( f(x) \) attains a maximum of 3 at \( x = 1 \). The value of the function at \( x = 0 \) is 1. What is the value \( f(x) \) at \( x = 10 \)?
A quadratic function \( f(x) \) attains a maximum of 3 at \( x = 1 \). The value of the function at \( x = 0 \) is 1. What is the value \( f(x) \) at \( x = 10 \)?
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When vertex form is known, directly substitute given point to find coefficient.
Updated On: Mar 23, 2026
- -119
- -159
- -110
- -180
- -105
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The Correct Option is A
Solution and Explanation
Let \( f(x) = a(x-1)^2 + 3 \) since maximum 3 occurs at \( x=1 \). For a maximum, \( a<0 \).
Given \( f(0) = a(0-1)^2 + 3 = a + 3 = 1 \) → \( a = -2 \).
Thus \( f(x) = -2(x-1)^2 + 3 \).
At \( x = 10 \): \( f(10) = -2(9^2) + 3 = -162 + 3 = -159 \) → matches option (2), not (1). Correction: Correct Answer is (2) -159.
Given \( f(0) = a(0-1)^2 + 3 = a + 3 = 1 \) → \( a = -2 \).
Thus \( f(x) = -2(x-1)^2 + 3 \).
At \( x = 10 \): \( f(10) = -2(9^2) + 3 = -162 + 3 = -159 \) → matches option (2), not (1). Correction: Correct Answer is (2) -159.
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