Question 1121358
Complete the square, adding 64 (half the 16 squared) to both sides
x^2-16x+64-48y-512=64
(x-8)^2-576=48y, rearranging.
(1/12)(x-8)^2-12=y, dividing by 48 both sides

The vertex is at (8,-12)

Some consider the form ax^2+bx+c=0 to be standard form.
This would be y=(1/12)x^2-(3/4)x-5/9

{{{graph(300,300,-50,50,-50,50,(1/12)(x-8)^2-12)}}}