1. Let the quadratic function be f (x) = ax 2+bx+c, because the image passes through point A and point B,

Then: a-b+c =-9, a+b+c =-1;

Because the function is tangent to the X axis, that is, AX 2+BX+C = 0 has only one root, then B 2-4ac = 0;

Solve with three equations: a =- 1, b = 4, c =-4; Or a=-4, b=4 and c=- 1.

So the resolution function is f (x) =-x 2+4x-4, or f (x) =-4x 2+4x-1.

2.f (x) = 1/5x 2-8/5x+3 This is a possible function.

3.( 1) Yes

If the function passes through point A and point B, then C = A, a+b+c =-2;

And the symmetry axis is x=2, that is,-b/2a = 2;

Solve with three equations: a = 1, b =-4, c =1;

The quadratic resolution function is f (x) = x 2-4x+ 1.

(2)|AB|= root number 5

4. This problem can't be solved, it should be a quadratic function, but the points are not standardized, and the accurate function expression can't be calculated!

But the optimum growth temperature should be between (-2,0).