I found the following sentence in my linear linear algebra book (affine and projective geometry): $Q:V \to \mathbb{K}$ is a quadric (quadratic function) and $\alpha\in Aff(V)$. $Aff(V)$ is the set of all affin and invertible functions $\alpha$.
The set of all centres of $Q\circ\alpha$ is bijective on the set of all centres of $Q$.
There is no proof so I tried to prove it, but I have not many ideas. I formulated the statement a little bit different; I need to show that $\sigma_{\alpha(m)}=\alpha\circ\sigma_m\circ\alpha^{-1}$ where $\sigma_m$ describes a reflection on $m\in V$.