# An algebra problem by K. J. W.

Algebra Level 4

Let $$f$$ be a real-valued function so that $$f(x) = a{ x }^{ 2 } + bx + c$$ for any real $$x$$, where $$a$$, $$b$$ and $$c$$ are distinct non-zero real numbers. If $$f(a) = b$$, $$f(b) = c$$, and $$f(c) = a$$, what is $$a + b + c?$$

×