What equation represents y=2x^2+24x+85 in vertex form

Y=a (x-h) ^2+k

vertex form is basically completing the square

what you do is

for

y=ax^2+bx+c

1. isolate x terms

y = (ax^2+bx) + c

undistribute a

y=a (x^2 + (b/a) x) + c

complete the square by take 1/2 of b/a and squaring it then adding negative and postive inside

y=a (x^2 + (b/a) x + (b^2) / (4a^2) - (b^2) / (4a^2)) + c

complete square

too messy /

anyway

y=2x^2+24x+85

isolate

y = (2x^2+24x) + 85

undistribute

y=2 (x^2+12x) + 85

1/2 of 12 is 6, 6^2=36

add neagtive and postivie isnde

y=2 (x^2+12x+36-36) + 85

complete perfect square

y=2 ((x+6) ^2-36) + 85

distribute

y=2 (x+6) ^2-72+85

y=2 (x+6) ^2+13

vertex form is

y=2 (x+6) ^2+13