Question

find an equation of a parabola with a vertex at the origin and directrix y=-2.5

Answer 1

so the general form of a parabola with a vertex at the origin is\[x^2 = 4ay\]

a is the focal length, the distance from the vertex to the directrix.

You also need to realise that the directrix is below the vertex so the prabola is concave up.

Answer 2

all you need to do is substitute the focal length into the general equation and simplify.