Question

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

Answer 1

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 $(y-k)^2=4p(x-h)$, 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: $(y-0)^2=4*4(x-0)$.  Cleaning that up a bit we get $y^2=16x$.  And there you go!