Repeat Exercise 57 but use -1, -2,...., -9 for the x-coordinates.

Exercise 57

It is possible to find a polynomial that goes through a given set of points in the plane by using a process called polynomial interpolation. Recall that three points define a second-degree polynomial, four points define a third-degree polynomial, and so on. The only restriction on the points, because polynomials define functions, is that no two distinct points can have the same x-coordinate.

Using the SSN 539-58-0954, we can find an eighth-degree polynomial that lies on the nine points with x-coordinates 1 through 9 and y-coordinates that are digits of the SSN: (1, 5), (2, 3), (3, 9), c , (9, 4). This is done by writing a system of nine equations with nine variables, which is then solved by the inverse matrix method. The graph of this polynomial is shown. Find such a polynomial using your own SSN.