A Uniform Bound on a Family

★ 8/10functions Extrema Absolute Value inequality Casework

Problem

Let $f(x) = ax^2 + |x - a| + b$ . Suppose that for every $b \in [0, 1]$ and every $x \in [-3, 3]$ ,

|f(x)| \leqslant 2.

Find the range of possible values of $a$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, Absolute Value, inequality, Casework

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