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   x =  v = speed   (instantaneous) 

   y = KE = 1/2 m  v²  = (m/2)  x²        instantaneous kinetic energy
      => x² =  2/m  y 

  This is in the form of    x² = (4a)  y    which is the standard equation for a parabola with y axis as the axis of the parabola and  (0,0) being the vertex of the parabola.  The directrix is given by  y = - a  = - 1/(2m)

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