Question

To fit a polynomial through n+1 data points, what degree must the polynomial be? Recall that a polynomial of degree LaTeX: nn has the form LaTeX: y = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_1 x + a_0.y = a n x n + a n − 1 x n − 1 + ⋯ + a 1 x + a 0 .

Answer 1

n

Explanation:

A polynomial of degree n will fit any n+1 data points that describe a function.

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Various interpolation methods have been developed to help you find the coefficients of the polynomial. Among them are "direct" and "Lagrange polynomial interpolation."