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这几年,在各省市的中考题中,出现了一些以体育运动为背景的中考试题,用以考查二次函数的有关知识.这类试题主要体现了数学知识与其它学科知识之间的变通性、统一性和实用性.这类试题的出现不仅增强了试题的趣味性,开拓了学生的视野,丰富了学生的知识,而且有利于培养学生应用数学知识的能力.一、足球例1在一场足球训练中,一名队员从球门正前方10米处练习挑射技术,当球被踢出后,运行的路线为抛物线.建立如图1所示的平面直角坐标系后,得抛物线的解析式为y=-1/12 x~2+7/6 x,已知球门框高为2.44米,请问如此射门能否进球?
In recent years, provinces and cities in the senior high school entrance examination questions, there have been some sports exams in the background of the test questions to test the quadratic function of knowledge .This type of test mainly reflects the mathematical knowledge and other disciplines of knowledgeable workarounds Sex, unity and practicality.The emergence of such questions not only enhances the interestingness of the test questions, opens up students 'horizons, enriches students' knowledge, but also helps students to develop their ability to apply mathematics knowledge. In a football training, a player practice the shooting technique 10 meters in front of the goal, and when the ball is kicked out, the course of running is a parabola. After establishing a plane rectangular coordinate system as shown in FIG. 1, a parabola The analytical formula is y = -1 / 12 x ~ 2 + 7/6 x, the known height of the goal frame is 2.44 meters. Is it possible to score such a goal?