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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