Rewrite the equation f (x) = 2x^2 + 12x+7 to the form f (x) = a (x-h) ^2+k

Complete theh square

isolate x terms

factor out coefient of x^2 term

take 1/2 of 1st degree coefient and square it, add positive and negative inside parnthasees, expand

f (x) = (2x^2+12x) + 7

f (x) = 2 (x^2+6x) + 7

6/2=3, 3^2=9

f (x) = 2 (x^2+6x+9-9) + 7

f (x) = 2 ((x+3) ^2-9) + 7

f (x) = 2 (x+3) ^2-19+7

f (x) = 2 (x+3) ^2-12