Parabola Construction

Manipulate[Module[{G, f = {0, 0}, m, P, t},
  If[tt < 4, t = tt - 2, t = 6 - tt];
  G = {t, -1};
  P = (G + f)/2;
  m = t;
  Show[Graphics[Join[
     {Line[{{-2, -1}, {2, -1}}], PointSize[Large], Red, Point[G],
      Blue, Point[f]}
     ], PlotRange -> {{-2.1, 2.1}, {-2, 2}}],
   If[tt >= 4,
    Table[
     Plot[(({\[Tau], -1} + f)/
          2)[[2]] + \[Tau] (x - (({\[Tau], -1} + f)/2)[[1]]), {x, -2,
       2}], {\[Tau], t, 2, 0.1}]
    ,
    Plot[P[[2]] + m (x - P[[1]]), {x, -2, 2}]
    ]
   ]
  ],
 {tt, 0, 8, 0.1}]