小题1:(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. 1 小题2:(Ⅱ)当时,抛物线为,且与轴有公共点. 对于方程,判别式≥0,有≤.·································· 2’ ①当时,由方程,解得. 此时抛物线为与轴只有一个公共点.·····························3’ 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. 4’ 小题3:(3)对于二次函数, 由已知时,;时,, 又,∴. 于是.而,∴,即. ∴. ·························································································· 5’ ∵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.·························· 6’ 又该抛物线的对称轴, 由,,, 得, ∴. ...………………………………………….7’ 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. 8’ |