parabolas

The directrix lies below the focus...so...this parabola turns upward....we can immediately rule out the last two answers

The vertex lies at (0, (-3 - 2) /2) =   (0, -5/2)

We have the form

4p ( y - k) =  (x -h)^2        where (h, k) is the vertex = (0, -5/2)

p is the distance between the focus and vertex = 1/2 units

So we have

4(1/2)(y - [- 5/2] ) = (x - 0)^2

2(y + 5/2) = x^2

2y + 5 = x ^2

2y = x^2 - 5      divide both sides by 2

y = (1/2)x^2 - 5/2