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The least-squares parabola uses a second degree curve

to approximate the given set of data, , , ..., , where . The best fitting curve has the least square error, i.e.,

Please note that , , and are unknown coefficients while all and are given. To obtain the least square error, the unknown coefficients , , and must yield zero first derivatives.

Expanding the above equations, we have

The unknown coefficients , , and can hence be obtained by solving the above linear equations.