f(0)=f(2)=3

The symmetry axis is x=(0+2)/2= 1.

The minimum value of the quadratic function f(x) is 1.

Let f(x)=a(x- 1)? + 1，a>0

∫f(0)= 3

∴a+ 1=3,a=2

∴f(x)=2(x- 1)？ + 1

=2x？ -4x+3

2.∫f(x) is not monotonic in the interval [2a, a+ 1].

The symmetry axis of f (x) is x= 1.

∴2a< 1

a+ 1> 1

∴0 2m- 1。

When x= 1, f (x) = 1 > 3+2m.

∴m