In addition to quadratic curves, we can also have more general (third degree) Bézier curves.
We've mentioned before the Bézier curve Wikipedia entry. Some interesting animations can be found on that page which explain how this works.
For a quick summary: A quadratic curve, which we saw before, is described by an equation of degree 2; a Bézier curve is described by an equation of degree 3. Thus, quadratic curves are special cases of Bézier curves. Whereas we needed one control point for a quadratic curve, we need two such control points to describe a general Bézier curve.
[The following table has been adapted from Wikipedia.]
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