Find the unique quadratic polynomial y = ax² +bx+c that passes through the three points (1, 1), (3,5), and (-2, 0) in the x-y plane. (Hint: this will involve a linear system where a, b, and c are the unknowns.) How many data points (x, y) should be needed to uniquely determine the coefficients of an nth degree polynomial anx" +an-1x²−¹+...+a₁x+ao? Explain your answer in terms of linear systems.

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