Minimum of absolute value of quadratic

Algebra Level 5

Consider all monic polynomials f(x)=x2+bx+cf(x) = x^2 + bx + c , where bb and cc are real numbers. What is the minimum value of NN, where

N=maxx[10,10]f(x)? 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)f(x) , as xx ranges from 10-10 to 1010 inclusive".

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