Question

3x^2+3x+2y=0 complete the square and reduce to one standard form y-b=A(x-a)^2 or x-a=A(y-b)^2

Answer 1

we are asked to transform the equation 3x^2+3x+2y=0 into the standard form by applying the technique of completing the square .

3(x^2+x +1/4) =-2y + 3/4
3 (x +1/2)^2 = -2 (y -3/8)
-3/2 (x +1/2)^2 = (y -3/8)
this follows the standard from y-b=A(x-a)^2

Answer 2

The required form is
`y-(3)/(8)=-(3)/(2)(x+(1)/(2))^2`

Explanation:

Given : Function
`3x^2+3x+2y=0`

To find : Complete the square and reduce to one standard form
`y-b=A(x-a)^2 \text{ or } x-a=A(y-b)^2`?

Solution :

Converting the functio into given standard form,

Taking y one side,
`-2y=3x^2+3x`

Divide by 3 both side,

`-(2)/(3)y=x^2+x`

Applying completing the square i.e. add half square both side,

`-(2)/(3)y+((1)/(2))^2=x^2+x+((1)/(2))^2`

`-(2)/(3)y+((1)/(2))^2=(x+(1)/(2))^2`

`(2)/(3)y-(1)/(4)=-(x+(1)/(2))^2`

Divide by
`(2)/(3)` both side,

`y-(3)/(8)=-(3)/(2)(x+(1)/(2))^2`

This form relates to
`y-b=A(x-a)^2`

Where,
`b=(3)/(8), A=-(3)/(2) ,a=-(1)/(2)`

Therefore, The required form is
`y-(3)/(8)=-(3)/(2)(x+(1)/(2))^2`