Find the equation of the parabola with vertex at (0,0) and focus at (0, 1/2)?

Answer 1

Y² = 4p(x)
Where p is the foci, 1/2
So:
Y² = 2x
Or: Y = √(2x)

Answer 2

The vertex and the focus both lie on the y-axis and the focus is above the vertex.

So equation is x^2=2py
The focus is at (0,p/2) so p/2= 1/2 --> p = 1
So equation is x^2=2y

Answer 3

Since the focus lies on the y axis ( positive ) and the vertex is the origin it is one of the standard parabolas.

Equation :

X^2 = 2 Y