Which of the following shows the equation y = x2 + 8x + 14 in vertex form?

A.

y = (x+4) 2 - 28

B.

y = (x+4) 2 - 2

C.

y = (x-8) 2 + 14

D.

y = (x+8) 2 + 14

Y=x²+8x+14

to make a square, if a is 1, add (half of b) ²

in this case, a=1, b=8, half of 8 is 4

y=x²+8x+4²-4²+14

y = (x+4) ²-16+14

y = (x+4) ²-2

B is the answer.

another way to do it:

the vertex is at x=-b/2a=-8/2*1=-4

when x=-4, y = (-4) ²+8 (-4) + 14=-2

so the equation is y=[x - (-4) ]²-2, which is y = (x+4) ²-2, the same answer B