Then the image of f(x) passes through points (0, 3),

Knowing that f(0)=3, that is, c=3,

∴f(x)=ax？ +bx+3；

Knowing that f(x) satisfies f(x+2)=f(2-x),

The function image is symmetrical about the straight line x=2, that is, -b/(2a)=2, ①.

Let the equation ax? Two of +bx+3=0 are s, t,

Then s+t= -b/a, st=3/a,

Judging from the meaning of the question, the sum of two squares =s? +t？ = 10,

That is (s+t)? -2st= 10，

∴(-b/a)？ -6/a= 10，②

From ① ② and a≠0, a= 1, b= -4,

The analytical formula of ∴f(x) is f(x)=x? -4x+3。