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把一个图形上的各点按同一方向移动同一距离的变换称为平移变换,平移变换是初中数学重要的思想和方法.我们知道平移变换不改变图形的形状和大小,只改变图形的位置.因此利用平移变换的这一特征,在解决有关二次函数问题时,可以有效整合图形(题设)信息,优化图形结构,使得较为复杂的问题得以创造性地解决.下面就采撷几例介绍这类问题的解法.1平移法解选择题例1(2010台州)如图1,点A,B的坐标分别为(1,4)和(4,4),抛物线y=a(x-m)2+n的顶点在线段AB上运动,与x轴交于C、D两点(C在D的左侧),点C的横坐标最小值为-3,则点D的横坐标最大值
Transforming each point of a graph in the same direction and moving it by the same distance is referred to as a translational transformation, which is an important idea and method of mathematics in junior high school.We know that the translational transformation does not change the shape and size of the figure, but changes the position of the figure This feature of translation transformation can effectively solve the problem of quadratic functions by integrating the information of the patterns and optimizing the structure of the graph so that more complicated problems can be creatively solved. (1), the coordinates of points A, B are respectively (1,4) and (4,4), the parabola y = a (xm) 2 + n The vertex moves on the AB segment of the line, intersects with the x axis at two points C and D (C is on the left side of D), and the minimum value of the abscissa of the point C is -3, then the maximum of the abscissa of the point D