The parabola opens rightwards,the focus $F$ is to the right of the vertex and the latus rectum is to the left.
Since $V$ lies on the parabola,distance of $V$ from the latus rectum $VZ=VF=a$ units.
The latus rectum is the chord through $F$ $\perp$ to $VF$
Therefore $a=2$ units.
The equation is of the form $Y^2=4aX$----(1)
Substitute these in eq(1) we get
$(y+1)^2=4\times 2\times (x-3)$
This is the required equation.