Question

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

Answer 1

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