Discrete minima - maxima problem

Question

Let $x,y_1,...,y_K$ be vectors in $\{-1,1\}^n$.Is it true that function $f:\{-1,1\}^n \rightarrow \mathbb{R} $ defined by following : $$f(x)=\sum_{k=1}^{K}<y_{k},x>^{2}$$ has local maximums in points $y_1,...,y_K$>.I think that this isn't true but can't find counterexample. Any help or hint would be appreciated.