摘要： 已知抛物线. (Ⅰ)若..求该抛物线与轴公共点的坐标, (Ⅱ)若.且当时.抛物线与轴有且只有一个公共点.求的取值范围, (Ⅲ)若.且时.对应的,时.对应的.试判断当时.抛物线与轴是否有公共点?若有.请证明你的结论,若没有.阐述理由． 解(Ⅰ)当.时.抛物线为. 方程的两个根为.． ∴该抛物线与轴公共点的坐标是和． ················································ 2分 (Ⅱ)当时.抛物线为.且与轴有公共点． 对于方程.判别式≥0.有≤． ········································ 3分 ①当时.由方程.解得． 此时抛物线为与轴只有一个公共点．································· 4分 ②当时. 时.. 时.． 由已知时.该抛物线与轴有且只有一个公共点.考虑其对称轴为. 应有 即 解得． 综上.或． ················································································ 6分 (Ⅲ)对于二次函数. 由已知时.,时.. 又.∴． 于是．而.∴.即． ∴． ············································································································ 7分 ∵关于的一元二次方程的判别式 . ∴抛物线与轴有两个公共点.顶点在轴下方．····························· 8分 又该抛物线的对称轴. 由... 得. ∴． 又由已知时.,时..观察图象. 可知在范围内.该抛物线与轴有两个公共点． ············································ 10分

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