1.平移二次函数 y=a(x-h)~2+k 的图象被平移时,开口大小和方向没有变,即二次项系数 a 不变,变化的只是它的位置,关键是顶点(h,k)的改变.因此抛物线的平移可以看作是顶点的平移,其规律可以概括为:平移变化在顶点.例1 抛物线 y=2x~2-8x+5向左平移4个单位,再向上平移2个单位,求平移后的解析式. 1. When the image of the translation quadratic function y=a(xh)~2+k is translated, the size and direction of the opening do not change, that is, the coefficient a of the quadratic term does not change, only its position is changed, and the key is the vertex ( h,k) change. So the translation of the parabola can be regarded as the translation of the vertex, and its rule can be summarized as: the translation change is at the vertex. Example 1 The parabola y=2x~2-8x+5 is translated to the left by 4 units, and then 2. Pan up 2 units and find the analytical formula after translation.