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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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    Yes, it is possible. In general, for any n points in a plane, you can find an (n-1)th degree (or higher) polynomial that passes through all of them. Finding these polynomial involves solving matrix equations and can sometimes get a bit messy.2012-02-10
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    You can also use a Lagrange interpolating polynomial.2012-02-10
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    @jpm 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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