有些数学习题,当直接解答或证明结论比较困难时,可以通过联想,灵活运用基本知识,打破常规．独辟蹊径．下举几例供参考．例1设k≠0,求证:抛物线y=kx2-(2k- 1)x+(k+2)恒过一定点,并求出该定点的坐标．分析因为定点是未知的,直接证明所有抛物线y=kx2-(2k-1)x+(k+2)都过某定点难以入手．但不同的抛物线对应于不同的k(k≠0)的值,故可以从关于k的方程有无多个解的情形加以讨论． Some mathematics problems, when directly answering or proving conclusions are more difficult, can be used to associate and use basic knowledge to break the convention. Unique way. Here are some examples for reference. Example 1 Let k ≠ 0, and verify that the parabola y=kx2−(2k−1)x+(k+2) is constant over a certain point, and the coordinates of the fixed point are found. Analysis Because the fixed point is unknown, it is directly proved that all parabolas y=kx2-(2k-1)x+(k+2) are difficult to reach after a certain fixed point. However, different parabolas correspond to different values ​​of k(k≠0), so we can discuss whether there are multiple solutions for the equation of k.