Question

3．拋物線y=-（x+1）²-2與拋物線y=（x+1）²+2關(guān)于x軸成軸對(duì)稱；拋物線y=-（x+1）²-2與拋物線y=-（x-1）²-2關(guān)于y軸成軸對(duì)稱．

Answer 1

分析 由關(guān)于x軸對(duì)稱點(diǎn)的特點(diǎn)是：橫坐標(biāo)不變，縱坐標(biāo)變?yōu)橄喾磾?shù)，可求出拋物線y=-（x+1）²-2關(guān)于x軸對(duì)稱的拋物線解析式；再由關(guān)于y軸對(duì)稱點(diǎn)的特點(diǎn)是：縱坐標(biāo)不變，橫坐標(biāo)變?yōu)橄喾磾?shù)，可得關(guān)于y軸對(duì)稱的拋物線解析式．

解答 解：∵y=-（x+1）²-2，
∴關(guān)于x軸對(duì)稱的拋物線解析式為-y=-（x+1）²-2，即y=（x+1）²+2；
∴關(guān)于y軸對(duì)稱的拋物線解析式為y=-（-x+1）²-2，即y=-（x-1）²-2．
故答案為y=（x+1）²+2；y=-（x-1）²-2．

點(diǎn)評(píng) 此題考查了二次函數(shù)的圖象與幾何變換，解題的關(guān)鍵是抓住關(guān)于x軸、y軸對(duì)稱點(diǎn)的特點(diǎn)．