Question

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?
y = 2 (x + seven-halves) squared minus one-fourth
y = 2 (x + seven-halves) squared minus one-half
y = 2(x + 7)2 – 73
y = (x + 7)2 – 24

Answer 1

First rewrite and complete the square:

y = (x + 3)^2 + (x + 4)^2
= 2x^2 + 14x + 25
= 2(x^2 + 7x) + 25
= 2[(x + 7/2)^2 - (7/2)^2] + 25
= 2(x + 7/2)^2 - 2*(49/4) + 25
= 2(x + 7/2)^2 - 24.5 + 25
= 2(x + 7/2)^2 + 1/2.

So the correct vertex form is y = 2(x + 7/2)^2 + 1/2. None of the four given choices match this.