Question: (a) (2 pts) Write down the linear system of equations for the coefficients of a quadratic polynomial f(x) : ax2+bx+c, that would interpolate the points

(a) (2 pts) 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, l), (-1, 4), (l, 2) and (3, -l). (b) (2 pts) Explain why the system you found in (a) is inconsistent (so no such polynomial exists). (c) (2 pts) Find the normal equation for the system you found in (a). (d) (2 pts) Find the polynomial of degree 2 that best ts the points in (a)

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