Question

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

y = 2(x + 7)2 – 73
y = (x + 7)2 – 24
y=2(x+(7/2))^2-(1/4)
y=2(x+(7/2))^2+(1/2)

Answer 1

The correct option is 4.

Explanation:

The given equation is

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

Simplify the above equation.

`y=x^2+6x+9+x^2+8x+16`
`[\because (a+b)^2=a^2+2ab+b^2]`

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

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

Add and subtract the value of
`((-b)/(2a))^2` in the above parenthesis.

`((-b)/(2a))^2=((-7)/(2(1)))^2=((7)/(2))^2`

`y=2[x^2+7x+((7)/(2))^2-((7)/(2))^2]+25`

`y=2[x+((7)/(2))]^2-2[((7)/(2))^2]+25`
`[\because (a+b)^2=a^2+2ab+b^2]`

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

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

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

Therefore correct option is 4.

Answer 2

y = (x + 3)2 + (x + 4)2= x²+9+6x+x²+16+8x=2x²+14x+25
y=2x²+14x+25
the vertex form of y=ax²+bx+c is y=a(x-h)²+k
where h= -b/2a
and k= c-b²/4a
so the vertex form is y=2(x-(-14/4))²+ 25-196/8=2(x+14/4)²+4/8=2(x+7/2)²+1/2
the answer is y=2(x+(7/2))^2+(1/2)