we know that
The parabola shown on the graph represent a vertical parabola open upward with vertex at the origin
so
the equation of the parabola is equal to
------> equation A
the equation of the directrix is equal to
![y=-a](/tpl/images/0357/8149/6519f.png)
In this problem we have
the equation of the directrix is equal to
![y=-1.5](/tpl/images/0357/8149/b6620.png)
so
the value of a is equal to
![a=1.5](/tpl/images/0357/8149/33e32.png)
substitute the value of a in the equation A
![x^{2}=4(1.5)y](/tpl/images/0357/8149/5a2be.png)
![x^{2}=6y](/tpl/images/0357/8149/69432.png)
therefore
the answer is the option
![x^{2} =6y](/tpl/images/0357/8149/bf65b.png)