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探究与抛物线有关的动线构造的图形之间的位置、数量关系等,是中考数学综合题的一般构造方式.由于问题的开放性较强,联系的知识点较多,富有趣味性、探究性的特点,因此倍受各地中考命题的重视.本文结合与动线、抛物线上动点构造的三角形相似问题进行分析,并得出一般问题的普遍性结论,供参考.一、问题引入例1如图1,点P是二次函数y=-x~2+3x的图象在y轴右侧部分上的一个动点,将直线y=-2x向上平移,分别与z轴、y轴交于点C、D,如果以CD为直角边的△PCD与△OCD相似,确定符合条件的点P的
To explore the relationship between the parabola-related lines and the graphics of the moving line structure is the general structure of the mathematics test questions in the senior high school entrance examination because of the openness of the question and the more knowledgeable points of contact, interesting and exploratory Therefore, it pays more attention to the examination questions in different places.According to the analysis of triangle similarities with moving line and parabola moving point, the general conclusions of general problems are given for reference.First, Figure 1: Point P is a moving point of the quadratic function y = -x ~ 2 + 3x on the right part of the y-axis. The straight line y = -2x is translated upward and is intersected with the z-axis and the y- Point C, D, if the PCD at the right-angled edge of the PCD and △ OCD similar to determine the conditions of the point P