taiwan-gsat 2024 Q5

taiwan-gsat · Other · gsat__math-b 5 marks Completing the square and sketching Max/min of a quadratic function on a closed interval with parameter

Let the quadratic function $f ( x ) = x ^ { 2 } + b x + c$, where $b , c$ are real numbers. Given that $f ( x - 2 ) = f ( - x - 2 )$ holds for all real numbers $x$, and when $- 3 \leq x \leq 1$, the maximum value of $f ( x )$ is 4 times its minimum value, what is the minimum value of $f ( x )$?
(1) 0
(2) $\frac { 5 } { 3 }$
(3) 3
(4) 4
(5) 6

Let the quadratic function $f ( x ) = x ^ { 2 } + b x + c$, where $b , c$ are real numbers. Given that $f ( x - 2 ) = f ( - x - 2 )$ holds for all real numbers $x$, and when $- 3 \leq x \leq 1$, the maximum value of $f ( x )$ is 4 times its minimum value, what is the minimum value of $f ( x )$?\\
(1) 0\\
(2) $\frac { 5 } { 3 }$\\
(3) 3\\
(4) 4\\
(5) 6

Paper Questions

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