Question

Rewritten in vertex form please!!! Asap!!!

Answer 1

B

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = (x + 3)² + (x + 4)² ← expand and simplify

= x² + 6x + 9 + x² + 8x + 16

= 2x² + 14x + 25

To obtain vertex form use the method of completing the square

The coefficient of the x² term must be 1

Factor out 2 from 2x² + 14x

y = 2(x² + 7x) + 25

add/ subtract ( half the coefficient of the x- term )² to x² + 7x

y = 2(x² + 2(
`(7)/(2)`) x +
`(49)/(4)` -
`(49)/(4)` ) + 25

y = 2(x +
`(7)/(2)` )² -
`(49)/(2)` +
`(50)/(2)`

y = 2(x +
`(7)/(2)` )² +
`(1)/(2)`

Answer 2

vertex form:
`y=2(x+(7)/(2))^2+(1)/(2)`

B correct

Explanation:

`y=(x+3)^2+(x+4)^2`

`y=x^2+9+6x+x^2+16+8x`

`y=2x^2+14x+25`

`y=2(x^2+7x)+25`

`y=2(x^2+7x+(49)/(4)-(49)/(4))+25`

`y=2(x+(7)/(2))^2+(1)/(2)`