20 1 1 the answer to the last question of mathematics in Hainan senior high school entrance examination should be sought in detail. . . . . . . .

(1) If the parabola passes through the origin, 9-b 2 = 0, that is, b = 3.

And because the fixed point m is in the first quadrant, according to the symmetry axis is greater than zero, b=3.

(2)① y =-x 2+3x from (1)

Vertex M(3/2, 9/4)

So the length of AB is an integer value of 1 or 2.

When AB= 1, BC is not an integer (truncation);

When AB=2, B (1, 0) c (2,0) is BC= 1.

So the circumference of the rectangular ABCD is 6.

(2) Let the abscissa of point A be X by the analytical formula E (3 3,0), then:

Circumference = 2 (3-2x)+2 (-x 2+3x)

=-2x^2+2x+6

=-2(x- 1/2)^2+ 13/2

So when x= 1/2, the maximum perimeter is 13/2, and at this time A( 1/2, 5/4).

③ Area = (3-2x) (-x 2+3x)

=x(x-3)(2x-3)