posted by Marissa .
write an equation for the parabola with focus (1,3) and vetex (0,3)
See the paragraph Analytic Geometry Equations. You will have a choice of equations, you did not state whether the axis of symettry was parallel to x or y axis.
that was all my question said.
Since your question was to "write" the equation, I would assume we don't have to do a rigorous solution.
From your data it is easy to see that the axis of symmetry is the line y=3, so it is parallel to the x-axis
If the vertex had been (0,0) and the focal point is (k,0) then the equation is y^2 = (4k)x
So if we "move" our parabola down 3 units, our vertex would be (0,0) and the focus would be (1,0)
so 4k=1 and k=1/4
then with vertex (0,0) our equation would be y^2 = (1/4)x
now lets translate this my "moving" it up 3 units
(y-3)^2 = (1/4)x