Clear[XY];
XY = {{0.,1.},{1.,0.},{2.,0.2}, {3.,1.}};
Clear[B,BX,BY];
B[t_] = XY[[1]]t^3+XY[[2]] 3t^2(1-t)+
             XY[[3]] 3t(1-t)^2 +XY[[4]] (1-t)^3;
BX[x_] = B[x][[1]];
BY[x_] = B[x][[2]];

Clear[dots];  
dots = ListPlot[XY,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
gr = ParametricPlot[{BX[t],BY[t]},{t,0,1},
     DisplayFunction->Identity];
txt = StringForm["Bezier Curve and Control Points"];
Show[gr,Graphics[Line[XY]],dots,
DisplayFunction->$DisplayFunction,
PlotLabel->txt];

Clear[XY];
XY = XY = {{0.,0.2},{1.,0.},{2.,0.2}, {3.,0.75},{4.,1.3},
       {5.,1.3}, {6.,1.}};
Clear[B1, BX1, BY1,B2, BX2,BY2];
B1[t_] = XY[[1]]t^3+XY[[2]] 3t^2(1-t)+
             XY[[3]] 3t(1-t)^2 +XY[[4]] (1-t)^3;
BX1[x_] = B1[x][[1]];
BY1[x_] = B1[x][[2]]; 
B2[t_] = XY[[4]] t^3+XY[[5]] 3t^2(1-t)+
             XY[[6]] 3t(1-t)^2+XY[[7]] (1-t)^3;
BX2[x_] = B2[x][[1]];  
BY2[x_] = B2[x][[2]];

dots = ListPlot[XY,PlotStyle->{PointSize[0.02]},
                DisplayFunction->Identity];
gr1 = ParametricPlot[{BX1[t],BY1[t]},{t,0,1},
     DisplayFunction->Identity];
gr2 = ParametricPlot[{BX2[t],BY2[t]},{t,0,1},
     DisplayFunction->Identity];
txt = StringForm["Bezier Curve and Control Points"];
Show[gr1,gr2,Graphics[Line[XY]],dots,
DisplayFunction->$DisplayFunction, 
PlotLabel->txt];