Manipulate the equation to get it in one of the following forms:
[tex] x^{2} = 4py[/tex] or [tex]y^2=4px[/tex]
Subtract 3y from both sides of the equation: [tex]6 x^{2} =-3y[/tex]
Divide by 6 on both sides of the equation (reduce): [tex] x^{2} =- \frac{1}{2}y[/tex]
This is a parabola that opens down and the value of p = [tex]- \frac{1}{8} [/tex].
The vertex is at the origin (0, 0)
Focus: (0, 0 + p) ⇒ [tex](0, - \frac{1}{8} )[/tex]
Directrix: y = 0 - p ⇒ [tex]y = \frac{1}{8} [/tex]
Axis of Symmetry: x = 0
