The vertex form of a parabola:
[tex]y=a(x-h)^2+k[/tex]
You have y². It's not a function. OK. But away, the graph is a parabola but it is horizontal parabola.
[tex]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)}[/tex]
Your answer is:
(x+4) = (y + 1)²
