Question

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

Answer 1

Explanation:

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