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I can define a curve that passes through 3 points using a quadratic equation:

ax2 + bx + c = 0 

I would like to know is it possible to define a curve that passes through 4 points using:

ax3 + bx2 + cx + d = 0 

Cheers

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    @jp$m$ is correct. For an easy formula (that works in *most* cases), see [Lagrange polynomial - Wikipedia, the free encyclopedia](http://en.wikipedia.org/wiki/Lagrange_polynomial).2012-02-10

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The answer was already in the comments upon migration: Use a Lagrange polynomial. The restriction "in most cases" is unnecessary; the Lagrange polynomial is completely general and yields a polynomial which interpolates the points as long as no two of them have the same $x$ coordinate; if they do, there can be no univariate function, polynomial or otherwise, that interpolates them.