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 coef- ficients of an nth degree polynomial anx"+an-1xn-1+...+ a₁x+ao? Explain your answer in terms of linear systems.

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