Unusual Functional Twist

Algebra Level 5

f(x+y)=f(x)+2xy+f(y)\large{f(x+y) = f(x) + 2xy + f(y)}

Let f:QRf: \mathbb Q \to \mathbb R be a function defined on the set of all rational numbers Q\mathbb Q satisfying the above functional equation for all x,yQx,y \in \mathbb Q and where f(1)=2015f(1) = 2015. Submit the value of f(20.15)f(20.15) upto three correct places of decimals as your answer.

Bonus : Generalize f(x)f(x).

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