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问题已知a是实数,函数f(x)=2ax~2+2x-3-a,如果函数y=f(x)在区间[-1,1]上有零点,求实数a的取值范围.本题是我们2018届高三学生一轮复习的一道变式训练题,它以二次函数的零点为背景,富含数学思想且有探究价值,回味无穷.下面,我回顾一下自己的探究过程,与同学们分享.1.初步探究首先,我是从二次函数根的分布角度对问题展开探究的.问题可以转化为:方程2ax~2+2x-3-a=0在区间[-1,1]上有实数根,于是
It is known that a is a real number and the function f(x) = 2ax~2+2x-3-a. If the function y=f(x) has a zero in the interval [-1,1], find the range of the real number a. This question is a variant exercise of our 2018 high school students’ review in the first round. It is based on the zero point of the quadratic function. It is rich in mathematics and has inquiring value. The following is endless. I recall my own inquiry process. Share with students 1. Preliminary exploration First, I explored the problem from the perspective of the distribution of quadratic function roots. The problem can be translated as: Equation 2ax~2+2x-3-a=0 in the interval [-1, 1] has a real number root, so