(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