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二次函数是中考的热点之一,许多同学动态分析能力较差,失误颇多.下面针对近年试卷上的错解举例剖析. 一、二次项系数为零致错例1 若二次函数y=(m2-4)x2+3x+1-m与一次函数y=(m2-2)x+m2-3的图象与y轴交点的纵坐标互为相反数,则m的值为__. 错解:由题设得(1-m)+(m2-3)=0,即m2-m- 2=0,解得m=2或m=-1. 剖析:当m=2时,m2-4=0,则函数y=(m2-4) x2+3x+1-m不是二次函数,所以还应结合m2-4≠0、m2-2≠0,即m≠±2、m≠±2~(1/2).
The quadratic function is one of the hot topics in the examination. Many students have poor dynamic analysis skills and many mistakes. The following example analyzes the mistakes on the examination papers in recent years. The first and second item coefficients are zero. Example 1 If the quadratic function y =(m2-4)x2+3x+1-m and the y=(m2-2)x+m2-3 image of the primary function and the ordinate of the y-axis intersection point are mutually opposite numbers, and the value of m is __ The wrong solution: from the question set up (1-m) + (m2-3) = 0, that is m2-m- 2 = 0, the solution was m = 2 or m = -1. Analysis: When m = 2, M2-4=0, the function y=(m2-4) x2+3x+1-m is not a quadratic function, so m2-4≠0, m2-2≠0 should also be combined, ie m≠±2,m ≠±2~(1/2).