Answer:
[tex]y=\dfrac{1}{8}(x-2)^2-4[/tex]
Step-by-step explanation:
The directrix y=-6 is parallel to the x axes, so parabola has equation of the form
[tex](x-x_0)^2=2px(y-y_0),[/tex]
where [tex](x_0,y_0)[/tex] is the vertex of parabola and p is parabola's parameter.
By the definition, [tex]\frac{p}{2}[/tex] is the distance from the vertex to the directrix, so
[tex]\dfrac{p}{2}=2\Rightarrow p=4[/tex]
Hence, the equation of parabola is
[tex](x-2)^2=8(y+4)[/tex]
See attached diagram for the graph of parabola and its directrix.
In vertex form this equation is
[tex]y=\dfrac{1}{8}(x-2)^2-4[/tex]
