c  =  
      ParametricPlot3D[{t^2, 1 - 3  t, 1 + t^3}, {t, -2, 3.1}]

pts  = 
      Graphics3D[{PointSize[0.04], RGBColor[0, 1, 0], Point[{1, 4, 0}], 
          RGBColor[0, 0, 1], Point[{9, -8, 28}], RGBColor[1, 0, 0], 
          Point[{4, 7, -6}]}]

Show[c, pts, ViewPoint -> {-1,  4,  1}]