The quadratic function f (x) satisfies that f (x + 2) = f (- x + 2), f (0) = 3, f (2) = 1. If there is a maximum value of 3 and a minimum value of 1 on [0, M], then the value range of m is () A. （0，+∞）B. [2，+∞）C. （0，2]D. [2，4]

The quadratic function f (x) satisfies that f (x + 2) = f (- x + 2), f (0) = 3, f (2) = 1. If there is a maximum value of 3 and a minimum value of 1 on [0, M], then the value range of m is () A. （0，+∞）B. [2，+∞）C. （0，2]D. [2，4]

∵ quadratic function f (x) satisfies f (2 + x) = f (2-x), and its axis of symmetry is x = 2. Let its equation be y = a (X-2) 2 + B ∵ f (0) = 3, f (2) = 1 ∵ 4A + B = 3B = 1. The analytic expression of a = 12, B = 1 function f (x) is y = 12 (X-2) 2 + 1 ∵ f (0) = 3, f (2) = 1, the maximum value of F (x) on [0, M] is 3, the minimum value is 1, ∵ m ≥ 2 and f (4) = 3. It is known from the properties of quadratic function In conclusion, 2 ≤ m ≤ 4 is obtained, so D is selected