Bring the coordinate values of b (2 2,0) and c (0 0,8) into the function, and get

4a+2b+c = 0 ①

c = 8 ②

What is the symmetry axis of a quadratic parabola? X=-b/2a, so

-b/2a = -2 ③

Why? ① ② ③ Form the de equation and get a= -2/3, b= -8/3 and c =8.

So the expression of parabola is? y = -2/3 x？ -8/3 x +8

(2)

Because the symmetry axis is x = -2 and the point B is (2,0), the point A is (-6,0).

As shown above, point F is the vertical line FG of AB, and the vertical foot is G.

Available AE =m, be = 8-m.

Because of EF∑AC, we can get FG:OC = BE:AB, that is, FG:8 = (8-m):8.

So FG = 8-m

From this, we can get:

S△ABC = 8×8/2 = 32

S△ACE = 8×m/2 = 4m

S△EFB = (8-m)？ /2

therefore

S△CEF =？ S△ABC -？ S△ACE-？ EFB

? = 32 -4m -？ (8 meters)? /2

? = 32 -4m -32 +8m -m？ /2

? = ? -m？ /2 +4m

That is, the relationship between s and m is S =? -m？ /2 +4m

(3)

S =？ -m？ /2 +4m = - 1//2(m？ -8m+ 16) +8 = - 1/2(m-4)？ +8

So s has a maximum value of S =8.

When m =4, the coordinate of point E is (-2,0), that is? △BCE is an isosceles triangle.

?

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