Question

What is the equation of the parabola in vertex form?
0=y^2– x+2y-3

Answer 1

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

Explanation:

The given parabola has equation
`0=y^2-x+2y-3`

We regroup to get:

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

We add and subtract the square of half the coefficient of the y-term.

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

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

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

We factor the perfect square trinomial to get:

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

`\implies (x+4)=(y+1)^2` ..... This is the vertex form