Is every 2-nd degree polynomial symmetric about its extremum? I took the general 2-nd degree polynomial $P(x) = ax^2 + bx + c$, computed $P'(x\_0) = 0 => x\_0 = -b/2a$, but then $P(x\_0 + d)$ and $P(x\_0 - d)$ are not equal. 

Is this evidence against my hypothesis? It seems like it is, however I might have done a mistake, and in any case my intuition tells me that symmetry indeed exists. Like, every 2-nd degree polynomial I have seen in my life was symmetric. Can someone confirm or disprove this?