运动变化是自然科学的一个普遍规律,更是函数研究的主要内容。利用运动和静止这一对矛盾的对立统一,从相对静止去研究运动规律是数学思想的重要方法之一,应引起人们足够的重视。这里笔者结合近年各地中考试题进行分析,希望对读者有所帮助。 例1 一条抛物线是由y=-x~2的图象经过平移得到的,它的顶点沿着曲线y=2x~2+x+1滑动,若它又经过点(1,4),求此抛物线的解析式。 (1997,江苏省盐城市中考题) The change of motion is a universal law of the natural sciences, and it is the main content of the function study. The use of the contradictory unity of motion and quiescence is one of the most important methods for studying mathematics from a relatively static point of view. It should attract people’s attention. Here the author combines the examination questions in various places in recent years to analyze and hope to help readers. Example 1 A parabola is obtained by translating the image of y=-x~2. Its vertex slides along the curve y=2x~2+x+1. If it passes through the point (1,4) again, Parabolic analytical formula. (1997, Yancheng City, Jiangsu Province)