I noticed something interesting while doing some homework on finding the vertex of a graph, and was wondering if anyone had an explanation for it.
Solving for $f(X) = A(X ^ 2) + BX$, I saw that for any numbers $A$ and $B$, plugging $X$ as the axis of symmetry would cause $A + B$ to equal $-A$
Random example: $f(X) = 7(X ^ 2) + 273X$
Plugging in the axis of symetry gives me $f(-19.5) = 7(-19.5 ^ 2) + 273(-19.5) = 2661.75 - 5323.5 = -2661.75$
I thought this seemed interesting :D