Answer:
[tex]y=\frac{1}{10}x^2[/tex]
Step-by-step explanation:
Since the directrix is [tex]y=-2.5[/tex], it means the axis of the parabola is parallel to the y-axis.
Also, the vertex is at the origin so the parabola opens upwards.
The equation of a parabola with these properties is of the form [tex]x^2=4py[/tex], where [tex]|p|=2.5[/tex],that is the distance between the vertex and the directrix.
[tex]\Rightarrow p=-2.5\:or\:2.5[/tex].
Since the parabola opens upwards, we choose [tex]p=2.5[/tex].
The equation of the parabola now becomes,
[tex]x^2=4(2.5)y[/tex]
[tex]\Rightarrow x^2=10y[/tex]
Or
[tex]y=\frac{1}{10}x^2[/tex]
See graph
