Three Values Bound a Quadratic

★ 7/10functions Quadratic Equations Absolute Value Completing the Square inequality

Problem

The quadratic $f(x) = ax^2 + bx + c$ ( $a \ne 0$ ) satisfies

|f(0)| \le 2, \qquad |f(2)| \le 2, \qquad |f(-2)| \le 2.

Find the maximum possible value of $|f(x)|$ over $x \in [-2, 2]$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Quadratic Equations, Absolute Value, Completing the Square, inequality

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