Click and drag control points to change curve. Modify weights in boxes below the curve.

For more information, check out the post on my blog: Bezier Curves.

W1
W2
W3

Rational quadratic bezier curves have 3 control points, a weight per control point (3 total), and total up the values of the 3 functions below to get the final point at time t.

A * W1 * (1-t)^2

B * W2 * 2t(1-t)

C * W3 * t^2

Then they divide by the total of these 3 functions.

W1 * (1-t)^2

W2 * 2t(1-t)

W3 * t^2

Parameters: t - "time", but in our case we are going to use the x axis value for t. A - The first control point, which is also the value of the function when x = 0. B - The second control point. C - The third control point, which is also the value of the function when x = 1. W1 - The weighting for control point A. W2 - The weighting for control point B. W3 - The weighting for control point C.

In this particular case, A, B and C are scalars, which makes the curve into the function:
y = (A * W1 * (1-x)^2 + B * W2 * 2x(1-x) + C * W3 * x^2) / (W1 * (1-x)^2 + W2 * 2x(1-x) + W3 * x^2)

Note that this bezier curve is 1 dimensional because A,B,C are 1 dimensional, but you could use these same equations in any dimension. Also,
these control points range from 0 to 1 on the X axis, but you could scale the X axis and/or the Y axis to get a different range of values.