So the problem goes,
The Secant Method for finding the root of a function f[x] uses two successive points xn, xn-1 to compute a projected root based on the secant line through xn-1 and xn. By using polynomial interpolation, design a "parabolic method" which fits a quadratic polynomial through three function values xn-2, xn-1 and xn.
Give an explicit formula for xn+1 in terms of (xn,f[xn]), (xn-1,f[xn-1]), (xn-2,f[xn-2])
I appreciate any advices and help!