It is known that the quadratic function f (x) = ax ^ 2 + BX holds f (x minus 4) = f (2 minus x) for any x belonging to R, and the image of the function passes through a (1,3 / 2) (1) to find the function Given that the quadratic function f (x) = ax ^ 2 + BX belongs to R for any x, f (x minus 4) = f (2 minus x) holds, and the image of the function passes through a (1,3 / 2) (1) find the analytic expression of the function y = f (x) (2) if the solution set of the inequality f (x minus t) is less than or equal to x [4, M], find the value of the real number T, M

(1) A = 1 / 2, B = 1; so f (x) = 1 / 2 × x ^ 2 + X;
(2) : F (x) when t is maximum

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