The distance from the vertex to the focus is called the P value. The P value is related to the coefficient of the squared term, a, by P = 1/(4a) for positive a or P = -1/(4a) for negative a. For this problem the P value is P = 2, so a = 1/8 or -1/8.
The line between the vertex and the focus is horizontal, so this is a "sideways" parabola and the quadratic form involves y. The fact that the vertex is to the right of the focus implies that the parabola opens to the left. Thus a = -1/8
The vertex from of the parabola is therefore
x = -(1/8) (y - 3)2 -2
