Given that the quadratic function f (x) of one variable satisfies the condition f (1 + x) = f (1-x), the maximum value of F (x) is 15, and the sum of two squares of F (x) = 0 is 17, find f (x)

Let f (x) = ax ^ 2 + BX + C symmetry axis X = 1, then - B / 2A = 1, (4ac-b ^ 2) / 4A = 15, X1 ^ 2 + x2 ^ 2 = (x1 + x2) ^ 2-2x1x2 = (- B / a) ^ 2-2c / a = 17. A = - 2, B = 4, C = 13. F (x) = - 2x ^ 2 + 4x + 13

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