Clear[x0,x1,x2,x3,y0,y1,y2,y3,t]
(* Defines the control points and the variable t *)
{x0,y0}={4,1};  (*Point P_0*)
{x1,y1}={28,48};  (*Point P_1*)
{x2,y2}={50,42};   (*Point P_2*)
{x3,y3}={40,5}; (*Point P_3*)

{x[t_],y[t_]}={x0*(1-t)^3+3*x1*t*(1-t)^2+3x2*t^2*(1-t)+x3*t^3, y0*(1-t)^3+3*y1*t*(1-t)^2+3*y2*t^2*(1-t)+y3*t^3};
BezierCurve=
ParametricPlot[{x[t],y[t]},
{t,0,1},
PlotStyle->{{Blue,Thickness[0.0015]}}, 
AspectRatio-> Automatic,
AxesLabel->{"x","y"}]

BezierCurveWithLineSegments=
ParametricPlot[{{x[t],y[t]},
{x0+(x1-x0)*t,y0+(y1-y0)*t},
{x1+(x2-x1)*t,y1+(y2-y1)*t},
{x2+(x3-x2)*t,y2+(y3-y2)*t}},
{t,0,1},
PlotStyle->{Blue,Purple,Red,Orange},
AspectRatio-> Automatic,AxesLabel->{"x","y"}]

Clear[x0,x1,x2,x3,x4,x5,x6,y0,y1,y2,y3,y4,y5,y6,t]
(* Defines the control points and the variable t *)
{x0,y0}={4,1}; (*Point P_0*)
{x1,y1}={28,48}; (*Point P_1*)
{x2,y2}={50,42}; (*Point P_2*)
{x3,y3}={40,5}; (*Point P_3*)
{x4,y4}={45,37}; (*Point P_4*)
{x5,y5}={23,43}; (*Point P_5*)
{x6,y6}={9,-4}; (*Point P_6*)

TwoBezierCurves=
ParametricPlot[{{x0*(1-t)^3+3*x1*t*(1-t)^2+3x2*t^2*(1-t)+x3*t^3, y0*(1-t)^3+3*y1*t*(1-t)^2+3*y2*t^2*(1-t)+y3*t^3},
(* First Bezier Curve *)

{x3*(1-t)^3+3*x4*t*(1-t)^2+3x5*t^2*(1-t)+x6*t^3, y3*(1-t)^3+3*y4*t*(1-t)^2+3*y5*t^2*(1-t)+y6*t^3}},
(* Second Bezier Curve *)

{t,0,1},
PlotStyle->{Blue,Green},
AspectRatio-> Automatic,
AxesLabel->{"x","y"}]

TwoBezierCurves=
ParametricPlot[{{x0*(1-t)^3+3*x1*t*(1-t)^2+3x2*t^2*(1-t)+x3*t^3, y0*(1-t)^3+3*y1*t*(1-t)^2+3*y2*t^2*(1-t)+y3*t^3},
(* First Bezier Curve in BLUE, control points P_0, P_1, P_2, P_3 *)

{x3*(1-t)^3+3*x4*t*(1-t)^2+3x5*t^2*(1-t)+x6*t^3, y3*(1-t)^3+3*y4*t*(1-t)^2+3*y5*t^2*(1-t)+y6*t^3},
(* Second Bezier Curve in GREEN, control points P_3, P_4, P_5, P_6 *)

{x0+(x1-x0)*t,y0+(y1-y0)*t},
(*Line from P_0 to P_1 *)

{x1+(x2-x1)*t,y1+(y2-y1)*t},
(* Line from P_1 to P_2 *)

{x2+(x3-x2)*t,y2+(y3-y2)*t},
(* Line from P_2 to P_3 *)

{x3+(x4-x3)*t,y3+(y4-y3)*t},
(* Line from P_3 to P_4 *)

{x4+(x5-x4)*t,y4+(y5-y4)*t},
(* Line from P_4 to P_5 *)

{x5+(x6-x5)*t,y5+(y6-y5)*t}
(* Line from P_5 to P_6 *)},
{t,0,1},
PlotStyle->{Blue,Green,Purple, Red,Orange, Brown,Cyan, Magenta, Pink},
AspectRatio-> Automatic,
AxesLabel->{"x","y"}]