( 1)

From y=？ x？ +bx+c and points a (0 0,8) and c (6 6,0) give C=8 and b= 14/3.

The function expression of parabola is y=? x？ + 14x/3+8？ .

(2)

①∫S =( 1/2)( 10？ m)msin∠ACB =( 1/2)(6/ 10)( 10？ m)m=？ (3/ 10)(m？ 5)? + 15/2,

When m=5, the maximum value of s is 7.5? ;

(2) ∵ Function y in E (? 4/3,0) and c (6 6,0),

∴l:？ X=7/3, so it can be assumed that when S is maximum, there is a point F(7/3, y), which makes the topic hold;

I also know that q is the midpoint of AC at this time. Q(3，4)，

And know that d is a point on a parabola. d(？ x？ + 14x/3+8，8)？ D( 14/3，8)。

When ∠ qdf = 90, that is |DF|? +|DQ|？ =|FQ|？ When,

( 14/3? 7/3)? +(8? y)？ +( 14/3? 3)? +(8? 4)? =(7/3? 3)? +(y？ 4)?

y=8+35/36≈8.97，

∴ The coordinate of the qualified point F is F (7/3,8+35/36);

When ∠ QFD = 90, that is |DF|? +|FQ|？ =|DQ|？ When,

( 14/3? 7/3)? +(8? y)？ +? (7/3? 3)? +(y？ 4)=? ( 14/3? 3)? +(8? 4)? ,

9y 108y+302=0，

y=6+√22/3？ 7.5634 or 6? √22/3≈4.4365,

∴ The coordinates of the qualified point F are F [7/3,6+(√ 22/3)]? , or f [7/3,6 (√ 22/3)];

When ∠ fqd = 90, that is |DQ|? +|FQ|？ =|DF|？ When,

( 14/3? 3)? +(8? 4)+? (7/3? 3)? +(y？ 4)=( 14/3? 7/3)? +(8? y)？ ,

y=4+5/ 18≈4.2778？ ,

∴ The coordinate of the qualified point f is f (7/3,4+5/18).

To sum up, the coordinates of the qualified point F * * * at four o'clock are:

F(7/3，8+35/36)、F(7/3，6+√22/3)？ 、F(7/3，6？ √22/3)、F(7/3，4+5/ 18)。