Y = X2 - 8X + 12
set to 0
X2- 8X + 12 = 0
X2 - 8X = - 12
halve the coefficient of the linear term, ( - 8 ), square it and add it to both sides
X2 - 8X + 16 = - 12 + 16
factor on the left and gather term on the right
(X - 4)2 = 4
(X - 4)2 - 4 = 0
================vertex form
(4, - 4)
=======vertex