A parabola with vertex can be transformed by the translation to one with the origin as vertex. A suitable rotation around the origin can then transform the parabola to one that has the axis as axis of symmetry. Hence the parabola can be transformed by a rigid motion to a parabola with an equation . Such a parabola can then be transformed by the uniform scaling into the unit parabola with equation . Thus, any parabola can be mapped to the unit parabola by a similarity..
A parabola with vertex can be transformed by the translation to one with the origin as vertex A suitable rotation around the origin can then transform the parabola to one that has the axis as axis of symmetry Hence the parabola can be transformed by a rigid motion to a parabola with an equation  Such a parabola can then be transformed by the uniform scaling into the unit parabola with equation  Thus any parabola can be mapped to the unit parabola by a similarity