Here's an interesting question. I'm aware of closed forms of cubic polynomials that go through 1 or 2 specific (x,y) points. Are there closed form versions for 3 or 4 points?(adsbygoogle = window.adsbygoogle || []).push({});

1 pt: [tex]y = a(x-x_0)^3 + b(x-x_0)^2 + c(x-x_0) + y_0[/tex]

2 pt: [tex]y = a(x-x_0)^2(x-x_1)\ +\ b(x-x_0)(x-x_1)^2 \ +\ \frac{y_0(x-x_1)^3}{(x_0-x_1)^3} \ +\ \frac{y_1(x-x_0)^3}{(x_1-x_0)^3}[/tex]

3 pt: [tex]y = \ ?[/tex]

4 pt: [tex]y = \ ?[/tex]

I don't think there are.

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# Cubic Ploynomial forms

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