( 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)。