What is the equation of the parabola that has a vertex at # (6, 2) # and passes through point # (3,20) #?
If we assume the desired parabola has a vertical axis,
then the vertex form of any such parabola is
Therefore our desired parabola must have the vertex form
Furthermore we know that the "additional point"
Plugging this value back into our earier version of the desired parabola, we get
If the axis of symmetry is not vertical:
 if it is vertical a similar process can be used working with the general form
 if it is neither vertical nor horizontal, the process becomes more involved (ask as a separate question if this is the case; in general you will need to know the angle of the axis of symmetry in order to develop an answer).