Question

Write an equation of a parabola that opens upward, has a vertex at the origin, and a focus at (0,2)

Answer 1

The standard equation of a parabola with vertex at origin and it's axis vertical is:

\[x^2 = 4ay\]
and the focus of this lies at (0,a)

So, find out 'a', since you have the coordinates of the focus.

Answer 2

in old notation parabola looks like
\[4p(y-k)=(x-h)^2\] since your vertex is at the origin, this becomes
\[4py=x^2\] and now all you need is \(4p\) since \(p=2\) you have \(4p=8\) and your parabola is
\[8y=x^2\]