巧用抛物线的轴对称性解题

• 作 者: 甘福宁
• 机 构: 江苏省南京市江宁区江宁中等专业学校,
• 出 处: 中学生数学
• 发表日期: 2014年18期
• 关键词: 对称点 轴对称图形 轴对称性 顶点坐标 二次函数 函数图像 对应值 交点坐标 江苏徐州 请看

抛物线y=ax2+bx+c是以直线x=-b/2a为对称轴的轴对称图形,不难得到如下结论:(1)抛物线上对称两点的纵坐标相等;反之,抛物线上纵坐标相同的两点是对称点.(2)如果抛物线交x轴于两点,那么这两点是对称点.(3)若设抛物线上对称两点的横坐标分别为x1、x2,则抛物线的对称轴x=x1+x22.

The parabola y = ax2 + bx + c is the axisymmetric graph with the straight line x = -b / 2a as the symmetry axis. It is not difficult to get the following conclusions: (1) The longitudinal coordinates of two symmetrical points on the parabola are equal; on the other hand, The same two points are symmetrical points. (2) If the parabola intersects the x-axis at two points, then the two points are symmetric points. (3) If the abscissa of symmetrical two points on the parabola is x1 and x2, then the parabola Symmetry axis x = x1 + x22.