Can someone explain to me why when expanding this vertex form equation does the $ah^2$ term get included with the $+k$ part?
As far as I can see it's a product of expanding the $a(x-h)^2$ part.
I can only presume it's to keep the form $ax^2+bx+c$.
tvm
You're correct, $(ah^2+k)$ is just a constant, so we slap it into the position of $c$!