Minimum of absolute value of quadratic

Algebra Level 5

Consider all monic polynomials $f(x) = x^2 + bx + c$, where $b$ and $c$ are real numbers. What is the minimum value of $N$, where

$N = \max_{x \in [-10,10]} \vert f(x) \vert?$

Details and assumptions

The last equation states: "The maximum value of the absolute value of $f(x)$ , as $x$ ranges from $-10$ to $10$ inclusive".

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