Convert a quadratic curve points to polynomial representation?

Question

I have the X,Y of 2 end points and 1 bezier point, of a Quadratic Bezier curve.

Using this data, how can I derive the polynomial representation of the curve?

_{(source: euclidraw.com)}

Answer 1

B(t) = (1-t) * (1-t) * B0 + 2 * (1-t) * t * B1 + t * t * B2