Write an equation for the parabola with a vertex at the origin and focus of (4,0)

We will first plot those points to see what type of parabola this is.  If the vertex is at (0, 0) and the focus is at (4, 0), this will be a parabola that opens to the right, since the parabola always curves around the focus.  The standard form for a parabola of this type is , where h and k are the coordinates of the vertex, and p is the distance between the vertex and the focus.  Our h and k are both 0, and our p distance is 4: .  Cleaning that up a bit we get .  And there you go!