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Parabola in a Square
We define the quadratic polynomial f by f(x) = x2 + b.x + c with b,c ∈ R .
Which constants b,c suit the constraint f: [-1,1] → [-1,1] ?
Hence, we are looking for all parabolas f(x) = x2 + b.x + c , whose graph for x ∈ [-1,1] lies completely in the square [-1,1]2 .