Geogebra 4th order bezier curve

Question

Please can you tell me how I can draw 4th order bezier curve in Geogebra?

I have these polynomial cubics

B0(t) = (1 - t)3,
B1(t) = 3t(1 - t)2,
B2(t) = 3t2(1 - t),
B3(t) = t3 

but with these I can draw only simple Bezier curve and I need 4th order bezier curve with 5 control points.

Answer 1

If you have endpoints A, E and control points B, C, D, you can create the 4th degree Bézier curve using this GeoGebra command:

Curve(t⁴ A + 4t³ (1 - t) B + 6t² (1 - t)² C + 4t (1 - t)³ D + (1 - t)⁴ E, t, 0, 1)

You can get the polynomials by multiplying the binomial coefficients with corresponding powers of t and (1-t), see explicit definition of Bézier curve on Wikipedia for details.