24、(20 1 1? Panzhihua) as shown in the figure, it is known that the image symmetry axis of quadratic function y=x2+bx+c is a straight line x= 1, and it has two different intersections with the x axis, one of which is (-1, 0).

(1) Find the relation of quadratic function;

(2) There is a point A on the parabola, and its abscissa is ﹣2. The straight line L passes through the point A and rotates around the point A, and the other intersection with the parabola is point B, and the abscissa of the point B satisfies ﹣ 2 < XB.

(3) Is there a point C on the parabola that makes the area of △AOC equal to the maximum area of △AOB in (2)? If yes, find the abscissa of point C; If it does not exist, explain why.

Test center: Quadratic function synthesis problem.

Special topic: comprehensive questions.

Analysis: (1) Just substitute the coordinates and symmetry axis of point A;

(2) Substituting y=0 to solve a quadratic equation with one variable;

(3) According to the properties of right triangle, let the coordinates of point P be (x,? X), the coordinates of q and h can be obtained from Pythagorean theorem; Substitute x= 1 or 3 to get another coordinate.

Solution: Solution: (1) Quadratic function y=x2+bx+c The symmetry axis of the image is a straight line x= 1, which passes through point A (- 1, 0).

Replace:? = 1, 1﹣b+c=0，

Solution: b =-2, c =-3,

So the relationship of quadratic function is: y = x2-2x-3;

(2) The coordinate of the intersection of parabola and Y axis B is (0,? ),

Let the analytical formula of straight line AB be y=kx+m,

∴? ,

∴? ,

∴ The analytical formula of straight line AB is y=? x﹣？ .

∵P is a moving point on the AB line,

The coordinates of point p are (x,? x﹣？ ).(0