Calculate polynomial coefficients, roots or zeros, maximum and minimum, points of inflection, and interpolate polynomial value, slope and curvature.
Polynomials can be calculated for linear (first order), quadratic (second order), cubic (third order), quartic (fourth order), quintic (fifth order), sextic (sixth order), septic (seventh order), octic (eighth order) or nth degree. For polynomials with all real roots, all roots can sometimes be solved simultaneously using the Durand Kerner method. In other cases solve for individual roots. The maximum or minimum points (slope equals zero) and the inflection points (curvature equals zero) can also be calculated. Use a plot page to plot the polynomial and identify the approximate root values if any.
Lagrange's method is used to interpolate between data points. This method is useful for interpolating between data points, but can give poor results when extrapolating outside the data range. Evenly spaced data points can result in cyclic behaviour.
Polynomial coefficients can be calculated from the real roots, and the nth coefficient. There are an infinite number of polynomials with the same roots. The nth coefficient is required in order to calculate unique coefficients. This method only applies if all of the roots are real. Polynomial coefficients can also be calculated from XZ data points.
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