Write the equation in standard form of the parabola with vertex (0,0) and focus (0,1/2)

Question

I don't understand how I should start. Can you please help me and explain this step by step? 

Answer 1

 

The Vertex is at (0.0)

The focus is at (9, 1/2)

The parabola opens up because the focus is above the vertex.

 

The base equation is:

 

      X² = 4py

 

The distance from the vertex to the focus is the sames as the variable "P" in the base equation.

 

      p = 1/2

 

So our equation is:

 

      x² = 4(1/2)y

      x²  = 2y

 

       y = (1/2)x²