y = (x + 3) 2 + (x + 4) 2 rewritten in vertex form

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

completet 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 squaer it and add the positive and negative inside

y=2 (x^2+7x+12.25-12.25) + 25

factor perfec 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 negat