Posted by serg on .
y = 4x2  12x + 9

what is the question ? 
Damon,
You want zeros of y or what?
if zeros:
4 x^2  12 x + 9 = 0
(2 x3)(2x3) = 0
x = 1.5, 1.5 double root
If vertex etc:
4 x^2 12 x = y  9
x^2  3 y = (1/4)(y9)
x^2  3 y + 9/4 = (1/4)y
(x1.5)^2 = y/4
vertex at (1.5 , 0) which we knew already