28.(20 1 1 Chengdu) As shown in the figure, in the plane rectangular coordinate system xOy, the two vertices A and B of △ABC are on the X axis, and the vertex C is on the negative semi-axis of the Y axis. Known | OA |: | OB | = 1: 5, |OB|=|OC|,. (2) Let E be a moving point on the parabola on the right side of the Y axis, the parallel lines of the X axis intersect the parabola at another point F, FG is perpendicular to the X axis at point G, and EH is perpendicular to the X axis at point H through point E, thus obtaining a right-angled EFGH. Then, when the right-angle EFGH is a square in the movement process of point E, the side length of the square can be obtained; (3) Is there a point m on the parabola that is different from B and C, so that the height of BC in △MBC is 0? If it exists, find the coordinates of point m; If it does not exist, please explain why. Test center: Quadratic function synthesis problem. Special topic: comprehensive questions. Analysis: (1) If OA=m, OB=OC=5m, AB=6m, if △ABC = AB×OC= 15, the value of m can be obtained, and the three coordinates of A, B and C can be determined, and the parabola intersection point can be set by the two coordinates of A and B, and substituted into the C coordinate; (2) Let the coordinates of point E be (m, m 2 ~ 4m ~ 5) and the parabola symmetry axis be x=2, and solve the equation according to 2(m2)= eh; (3) existence. Because OB=OC=5, △OBC is an isosceles right triangle, and the analytical formula of straight line BC is y=x﹣5, then the distance from straight line y=x+9 or straight line y=x﹣ 19 to BC is 7. Combine the analytical formula of straight line with the analytical formula of parabola to find the coordinates of point M. Let OA=m, then OB=OC=5m and AB=6m. From △ABC = AB×OC= 15, we get ×6m×5m= 15, and the solution is m= 1 (. The analytical formula of ∴ parabola is y = (x+1) (x ? 5), that is, (2) let the coordinate of point e be (m, m 2-4m-5), the symmetry axis of parabola be x=2, and let 2 (m 2) = eh, 2 (m 2-2m-5). (3) existence. According to (1), OB=OC=5, ∴△OBC is an isosceles right triangle, and the analytical formula of straight line BC is y = x-5. According to the meaning of the question, straight line y=x+9 or straight line y = x-0/9 and BC. 16). Comments: This topic examines the comprehensive application of quadratic functions. The key is to use the method of combining shape and number to accurately express the length of line segment with the coordinates of points. According to the characteristics of graphics, solve equations and pay attention to classified discussion.