Make a sprite follow a bezier curve?

I'm trying to get a sprite to follow a bezier curve starting at the sx,sy start point and going thru to ex,ey (end). There are 2 points that influence the curve (p1 and p2). Anyone know how to do this before I pull out all my hair?

Insead of ploting the curve points, paste the sprite there.

Well that's kinda what I did, but you have to just keep feeding the function your new time along the curve. Which if you take (1.0 / number of seconds you want this to take) * delta time....then it works really good.

Graphics 800,600,0,0

Local sx:Float, sy:Float
Local ex:Float, ey:Float
Local p1x:Float, p1y:Float
Local p2x:Float, p2y:Float

'Start Point
sx = 100
sy = 300

'End Point
ex = 300
ey = 500

'Control Points
p1x = sx
If sy<ey Then p1y = sy-200 Else	p1y = ey-200
p2x = ex
p2y = p1y

Local fTimer:Float

While Not KeyHit(KEY_ESCAPE)
Cls

DrawText "S:  "+sx+", "+sy,5,5
DrawText "E:  "+ex+", "+ey,5,25
DrawText "P1: "+p1x+", "+p1y,5,45
DrawText "P2: "+p2x+", "+p2y,5,65

fTimer :+ (1.0 / 1.0) * 0.0005

If fTimer < 1 Then Bezier(sx,sy,ex,ey,p1x,p1y,p2x,p2y,fTimer)

Flip
Wend

Function Bezier(sx:Float,sy:Float,ex:Float,ey:Float,p1x:Float,p1y:Float,p2x:Float,p2y:Float,t:Float)
	Local pointx:Float = sx*(1-t)^3 + 3*p1x*(1-t)^2*t + 3*p2x*(1-t)*t^2 + ex*t^3
	Local pointy# = sy*(1-t)^3 + 3*p1y*(1-t)^2*t + 3*p2y*(1-t)*t^2 + ey*t^3
	Plot pointx,pointy
End Function