Given that the maximum value of quadratic function y = f (x) is equal to 13, and f (3) = f (- 1) = 5, then the analytic expression of F (x) is f (x)=______ ．

∵ the maximum value of quadratic function y = f (x) is equal to 13, and f (3) = f (- 1) = 5, the symmetry axis of the function is: x = 1, that is, f (x) = a (x-1) 2 + 13 ∵ f (3) = 4A + 13 = 5 ∵ a = - 2, then f (x) = - 2 (x-1) 2 + 13 = - 2x2 + 4x + 11, so the answer is: - 2x2 + 4x + 11

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