(2009?佛山)(1)请在坐标系中画出二次函数y=-x2+2x的大致图象;(2)在同一个坐标系中画出y=-x2+2x的 (1)请在坐标系中画出二次函数y=-x 2 +2x的大致图象...
\uff081\uff09\u8bf7\u5728\u5750\u6807\u7cfb\u4e2d\u753b\u51fa\u4e8c\u6b21\u51fd\u6570y=-x2+2x\u7684\u5927\u81f4\u56fe\u8c61\uff1b\uff082\uff09\u5728\u540c\u4e00\u4e2a\u5750\u6807\u7cfb\u4e2d\u753b\u51fay=-x2+2x\u7684\u56fe\u8c61\u5411\u4e0a\u5e73\u79fb\u4e24\uff081\uff09y=-\uff08x-1\uff092+1\uff0c\u5982\u56fe\uff0c\u5f53x=0\u65f6\uff0cy=0\uff1b\u5f53y=0\uff0c-x2+2x=0\uff0c\u89e3\u5f97x1=0\uff0cx2=2\uff0c\u5373\u629b\u7269\u7ebf\u4e0ey\u8f74\u7684\u4ea4\u70b9\u5750\u6807\u4e3a\uff080\uff0c0\uff09\uff0c\u4e0ex\u8f74\u7684\u53e6\u4e00\u4ea4\u70b9\u5750\u6807\u4e3a\uff082\uff0c0\uff09\uff0e\uff082\uff09\u5982\u56fe\uff0c
\uff081\uff09\u2235\u629b\u7269\u7ebfy=-x 2 +2x=-\uff08x-1\uff09 2 +1\uff0c\u2234\u9876\u70b9\u5750\u6807\u4e3a\uff081\uff0c1\uff09\uff0c\u5f00\u53e3\u5411\u4e0b\uff0c\u8fc7\u539f\u70b9\uff0c\u753b\u56fe\u5982\u4e0b\uff1a \uff082\uff09\u56fe\u8c61\u5411\u4e0a\u5e73\u79fb2\u5355\u4f4d\uff0c\u628a\u5404\u70b9\u7684\u7eb5\u5750\u6807\u52a02\uff0c\u6a2a\u5750\u6807\u4e0d\u53d8\uff0c\u753b\u56fe\u5982\u4e0b\uff1a \uff083\uff09\u5411\u4e0a\u5e73\u79fb2\u4e2a\u5355\u4f4d\u540e\u7684\u89e3\u6790\u5f0f\u4e3ay=-x 2 +2x+2\uff0e
(1)∵抛物线y=-x2+2x=-(x-1)2+1,∴顶点坐标为(1,1),开口向下,过原点,画图如下:
(2)图象向上平移2单位,把各点的纵坐标加2,横坐标不变,画图如下:
(3)向上平移2个单位后的解析式为y=-x2+2x+2.
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