vertex form is y=a(x-h)^2+k
expand and combine like terms and complete the square
expand
y=x^2+6x+9+x^2+8x+16
add
y=2x^2+14x+25
complete the square
first move 25 off to side
y=(2x^2+14x)+25
work inside
we need 1 in front of x^2
undistribute 2
y=2(x^2+7x)+25
take 1/2 of 7 and square it and add the positive and negative inside
y=2(x^2+7x+12.25-12.25)+25
factor perfect square inside
y=2((x+3.5)^2-12.25)+25
distribute the -12.25
y=2(x+3.5)^2-24.5+25
add
y=2(x+3.5)^2+0.5
add positive and negative