# Find coefficients of a polynomial given several points on its plot

For a polynomial of order n with unknown coefficients, what are the ways to find the coefficients from n+1 points on its plot?

I remember one way is to construct a fractional for each point, and the polynomial is the sum of the fractionals, s.t. for each fractional, its value is the desired value for its corresponding point and zero for other points. Is there a name for the method?

Thanks!

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The method you are talking about is called Lagrange Interpolation. If you want to find out the individual coefficients in the original "basis", then you would need to solve a $(n+1) \times (n+1)$ Linear system.