Calculate & Draw Bezier Curve: Red & Blue Handles

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The discussion centers on calculating and drawing Bezier curves, specifically those with two handles, referred to as red and blue. Participants seek equations and guidance on how to implement these curves, questioning if the depicted curve qualifies as a Bezier curve. There is a request for expert assistance, with an offer of payment for personalized teaching. The conversation highlights a need for clarity on Bezier curve theory and practical application. Overall, the thread emphasizes a desire for knowledge and support in mastering Bezier curves.
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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.
 
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Anyone expert on Bezier Curve theory?

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

I will pay.
 

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