There are many fourth editions of Challenging the Mathematics Final Exam. Here are some good functions and geometry problems for you. 1. Example 27 Question 23 of the senior high school entrance examination in Henan Province, as shown in figure 1, in the plane rectangular coordinate system, it is known that the parabola passes through three points: A (-4,0), B (0 0,4) and C (2 2,0). (1) Find the analytical formula of parabola. (2) If the point M is a point on the parabola of the third quadrant, the abscissa of the point M is M, and the area of Δ δAMB is S, find the functional relationship between S and M, and find the maximum value of S; (3) If point P is a moving point on a parabola and point Q is a moving point Y=-X on a straight line, can even positions make a quadrilateral with vertices P, Q, B and O a parallelogram? Write the coordinates corresponding to Q point directly. The answer is short for the time being, so you can draw your own picture. Answer: (1)Y= 1/2X? 0? 5+X-4。 (2)S=-m？ 0? 5-4m； (-4 < m < 0)； When m=-2, the maximum value of S is 4 (3) q1(-4,4); Q2(4，-4)； Q3(-2+2 radical 5,2-2 radical 5,4 (-2-2 radical 5,2+2 radical 5): Can a quadrilateral with points P, Q, B and O become a right-angled trapezoid? Please refer to this book for details. This is a good book. They are sold in all major bookstore streets. -thank you ~!