Unusual Functional Twist

Algebra Level 5

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

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

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

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