What is y=2x^2-12x+16 in vertex form

y = 2 (x-3) ^2 - 2

Step-by-step explanation:

y = 2x^2 - 12x + 16

y = 2 (x^2 - 6x + 8)

y = 2 (x^2 - 6x + 8 + 1 - 1) you "complete the square" by bringing the last term (8) up to "half of the middle co-efficient squared". Middle co-efficient is - 6, half is - 3, squared is 9. To get from 8 to 9 you must add 1 (+1), but if you add 1 you must subtract 1 (-1) so that you don't change the overall value of inside the bracket

y = 2 (x^2 - 6x + 9) - 2 (bring the - 1 outside of the brackets)

y = 2 (x-3) ^2 - 2