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一元二次方程ax2+bx+c=0(a≠0)与二次函数y=ax2+bx+c的联系在初三代数教材中很少涉及。笔者认为在课堂教学中适当给学生补充这方面的知识,对开阔学生的眼界,激发学生的学习兴趣不无裨益。归纳起来,一元二次方程与二次函数的联系有以下几个方面:①二次函数y=ax2+bx+c与X轴的交点情况,可以由对应的一元二次方程根的判别式△来确定:△>0 抛物线与X轴有2个交点;△=0 抛物线
The connection between the one-dimensional quadratic equation ax2+bx+c=0(a≠0) and the quadratic function y=ax2+bx+c is seldom involved in the third-generation algebra textbooks. The author believes that it is appropriate for students to supplement this knowledge in classroom teaching. It is not only helpful to broaden the horizons of students and inspire students’ interest in learning. To sum up, the relationship between the quadratic equation and the quadratic function has the following aspects: 1 The intersection of the quadratic function y=ax2+bx+c and the X-axis can be determined by the corresponding univariate quadratic equation. To determine: △>0 Parabola and X axis have 2 intersections; △=0 Parabola