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二次函数是刻画和研究现实世界数量关系及其变化规律的数学模型.生活中的问题历来是二次函数命题的重点.一、求距离例1(2012年绍兴卷)教练对小明推铅球的录像进行技术分析,发现铅球行进高度y(m)与水平距离x(m)之间的关系为y=-112(x-4)2+3,如图1,由此可知铅球推出的距离是m.解题思路:铅球落地时的高度为0,即y=0,铅球推出的距离为抛物线与x轴的正半轴交点的横坐标,求出方程-112(x-4)2+3=0的根即可.
The quadratic function is a mathematical model that characterizes and studies the relationship between the number of the real world and its changing rules. The problem in life has always been the focus of the quadratic function proposition. First, the distance example 1 (Shaoxing, 2012) coaches shot the ball for Xiaoming. Video analysis of the technology found that the relationship between shot height y(m) and horizontal distance x(m) is y=-112(x-4)2+3, as shown in Fig. 1. It can be seen that the distance from shot put is m. Problem solving ideas: The height of the shot putdown is 0, that is y = 0. The distance from which the shot is pushed is the abscissa of the intersection of the parabola and the positive semi-axis of the x-axis, and the equation -112(x-4)2+3 is obtained. =0 root can.