Related analytic expressions of quadratic function The function f (x) satisfies the following conditions （1）f（1+x）=f（1-x） (2) The maximum value of F (x) is 15 (3) The sum of two cubes of F (x) = 0 equals 17 Find the analytic expression of F (x)

First, Let f (x) = ax ^ 2 + BX + C be obtained from (1), f (x) be symmetric with respect to x = 1, so - B / 2A = 1, B = - 2AF (x) = ax ^ 2-2ax + C be obtained from (3), x1 ^ 3 + x2 ^ 3 = 17, that is, (x1 + x2) [(x1 + x2) ^ 3-3x1x2] = 17 (I) for f (x) = 0x1 + x2 = 2, X1 + x2 = C / A, substitute (I) to get C = - 3A / 2, then f (x) = ax ^ 2-2ax

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