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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