(1) Because the image passes through (0,0), the vertex coordinate is (2,8/3), and the symmetry axis is x=2, so the other intersection coordinate of the image and the y axis is (4,0).

Let the analytic expression of the function be y=a(x-0)*(x-4) and bring (2,8/3) into y =-2/3x 2+8/3x.

(2) Let the coordinates of point A be (c, 0) and point D be (c, -2/3c 2+8/3c).

So the side length of a square is AD =-2/3c 2+8/3c. Because AO=c, AB=2(2-c) because AB=AD.

So put the above two formulas together, c 1= 1, c2=6, because AB < 4, c= 1, so AB=2(2- 1)=2.