deutsche Version

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 .




Solution