Interpolating polynomials

Given a set of points with different $x$-values, there is a unique polynomial of degree at most $n$ that passes through all $n+1$ points. This polynomial is called the interpolating polynomial.

Important properties

• The interpolating polynomial matches the given $y$-values at the specified $x$-values.

• The degree of the interpolating polynomial is at most one less than the number of points.

• The polynomial is unique for a given set of points with distinct $x$-values.