How to calculate and draw a Bezier curve with control handles

[k8physics]

Could anyone mind to help me how to calculate and draw the curve such as below image?

http://s9.postimage.org/ksup6knwv/curve.png

There are two handles, the red and blue.

Also, is this everyone called by a Bezier curve?

Give me the equations and let me try to calculate by myself.

 

[k8physics]

Anyone expert on Bezier Curve theory?

If yes, I would like him/her to be my teacher.

I will pay.