Verified answer

Domain is all x:

The axis of symmetry is at 6/(2a) = 3/a

To find min/max value sub x=3/a

a(3/a)² - 6(3/a) + 4

= 4 - 9/a

The range is therefore, either

y >= 4 - 9/a, if a>0

y <= 4 - 9/a, if a<0

Zeroes, you can solve using quadratic formula:

x = ( 3 ± √(9 - 4a) ) / a