A Boundary Hunt

★ 8/10functions Quadratic Equations Absolute Value inequality Casework

Problem

Let $f(x) = ax^2 + 4x - 2$ . Suppose the real number $a$ can be chosen so that

|f(x)| \leqslant 4 \qquad \text{for all } x \in [m, 0].

Find the minimum possible value of $m$ , and the value of $a$ that achieves it.

Answer

Solution

Difficulty	8/10
Topics	functions, Quadratic Equations, Absolute Value, inequality, Casework

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