Question

Convert the equation to the standard form for a parabola by completing the square on x or y as appropriate. Can I get some help? y2 + 2y - 2x - 3 = 0

Answer 1

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

Explanation:

`y^2+2y-2x-3=0`

Since we have `y^2` and not `x^2` we complete the square on `y`

Place a bracket around the terms containing `y`

`(y^2+2y)-2x-3=0`

Add the square of half the coefficient of `y` inside the bracket and subtract this from outside the bracket:

`(y^2+2y+(1)^2)-(1)^2-2x-3=0`

simplify outside of bracket:

`(y^2+2y+(1)^2)-2x-4=0`

Convert `(y^2+2y+(1)^2)` into the square of a binomial:

`(y+1)^2-2x-4=0`

Factor:

`(y+1)^2-2(x+2)=0`

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

Answer 2

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

Explanation:

`"completing the square on "y^2+2y`

`• " add/subtract "(1/2"coefficient of the y-term")^2" to"`
`y^2+2y`

`y^2+2(1)ycolor(red)(+1)color(red)(-1)-2x-3=0`

`rArr(y+1)^2-1-2x-3=0`

`rArr(y+1)^2-2x-4=0`

`rArr(y+1)^2-2(x+2)=0`

`rArr(y+1)^2=2(x+2)`