1) Write down the linear system of equations for the coefficients of a quadratic polynomial f(x) = ax2+bx+c, that would interpolate the points (-2, 1), (-1, 4), (1, 2) and (3, -1).  2) Explain why the system you found in (a) is inconsistent (so no such polynomial exists). 3) Find the normal equation for the system you found in (a).

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter11: Matrices And Determinants
Section11.1: Matrices And Systems Of Linear Equations
Problem 1E: If a system of linear equations has infinitely many solutions, then the system is called _______. If...
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1) Write down the linear system of equations for the coefficients of a quadratic polynomial f(x) = ax2+bx+c, that would interpolate the points (-2, 1), (-1, 4), (1, 2) and (3, -1). 

2) Explain why the system you found in (a) is inconsistent (so no such polynomial exists).

3) Find the normal equation for the system you found in (a).

4) Find the polynomial of degree 2 that best fits the points in (a). 

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