Question 189971
Vertex form is:
y= a(x-h)^2+k
. 
y = x^2 + 7x + 12
y = (x^2 + 7x + __ ) + 12  -  __
.
Fill the blank with 1/2 of 'b' coefficient squared:
((1/2)(7))^2 = (7/2)^2 = 49/4
.
y = (x^2 + 7x + 49/4 ) + 12 - 49/4
y = (x^2 + 7x + 49/4 ) + 48/4 - 49/4
y = (x^2 + 7x + 49/4 ) - 1/4
y = (x + 7/2)^2 - 1/4  (this is what they're looking for)