Given that f (x) is a quadratic function, and f (2 + x) is an even function, and f (0) = 3, f (2) = 1, f (x) takes the maximum value of 3 and the minimum value of 1 on [0. M], then the value range of M is obtained

Given that f (x) is a quadratic function, and f (2 + x) is an even function, and f (0) = 3, f (2) = 1, f (x) takes the maximum value of 3 and the minimum value of 1 on [0. M], then the value range of M is obtained

F (x) is a quadratic function, and f (2 + x) is an even function,
On the symmetry of line x = 2, Let f (x) = a (X-2) &# 178; + n
And f (0) = 3, f (2) = 1,
4a+n=3,n=1 a=1/2,n=1
f(x)=(1/2)(x-2)²+1
The maximum value of F (x) in [0. M] is 3, and the minimum value is 1,
2≤m≤4
The range of M is [2,4]