Question

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

Answer 1

Answer:

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

Step-by-step 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