Question

What is the equation of the parabola in vertex form?

Answer 1

The vertex form of a parabola:

$y=a(x-h)^2+k$

You have y². It's not a function. OK. But away, the graph is a parabola but it is horizontal parabola.

$y^2-x+2y-3=0\ \ \ \ |+x+3\\\\y^2+2y=x+3\\\\y^2+2\cdot y\cdot1=x+3\ \ \ \ |+1^2\\\\\underbrace{y^2+2\cdot y\cdot1+1^2}_{use:(a+b)^2=a^2+2ab+b^2}=x+4\\\\\boxed{(y+1)^2=(x+4)}$

Your answer is:

(x+4) = (y + 1)²