已知二次函数y=x²-2x-3. （1）求函数图象的对称轴和顶点坐标； （2）当x∈[-2，3]时 已知二次函数y=x2-2x-3（1）求图象的开口方向、对称轴...
\uff082013?\u5e38\u5dde\u6a21\u62df\uff09\u5df2\u77e5\uff1a\u4e8c\u6b21\u51fd\u6570y=-x2+2x+3\uff081\uff09\u6c42\u629b\u7269\u7ebf\u7684\u5bf9\u79f0\u8f74\u548c\u9876\u70b9\u7684\u5750\u6807\uff1b\uff082\uff09\u753b\u51fa\u51fd\u6570\u56fe\u8c61\uff1b\uff083\uff081\uff09y=-x2+2x+3=-\uff08x2-2x+1-4\uff09=-\uff08x-1\uff092+4\u5bf9\u79f0\u8f74\u4e3a\u76f4\u7ebfx=1\uff0c\u9876\u70b9\u5750\u6807\u4e3a\uff081\uff0c4\uff09\uff0e\uff082\uff09\u629b\u7269\u7ebf\u4e0ex\u8f74\u4ea4\u4e0e\uff08-1\uff0c0\uff09\u548c\uff083\uff0c0\uff09\uff0c\u4e0ey\u8f74\u4ea4\u4e0e\u70b9\uff080\uff0c3\uff09\u56fe\u8c61\u4e3a\uff1a\uff083\uff09\u2460\u5f53y\u4e3a\u6b63\u6570\u65f6\uff0c-1\uff1cx\uff1c3\u2461\u5f53-2\uff1cx\uff1c2\u65f6\uff0c-5\uff1cy\uff1c4\uff1b
\uff081\uff09\u2235a=1\uff1e0\uff0c\u2234\u56fe\u8c61\u5f00\u53e3\u5411\u4e0a\uff1b\u2235y=x2-2x-3=\uff08x-1\uff092-4\uff0c\u2234\u5bf9\u79f0\u8f74\u662fx=1\uff0c\u9876\u70b9\u5750\u6807\u662f\uff081\uff0c-4\uff09\uff1b\uff082\uff09\u7531\u56fe\u8c61\u4e0ey\u8f74\u76f8\u4ea4\u5219x=0\uff0c\u4ee3\u5165\u5f97\uff1ay=-3\uff0c\u2234\u4e0ey\u8f74\u4ea4\u70b9\u5750\u6807\u662f\uff080\uff0c-3\uff09\uff1b\u7531\u56fe\u8c61\u4e0ex\u8f74\u76f8\u4ea4\u5219y=0\uff0c\u4ee3\u5165\u5f97\uff1ax2-2x-3=0\uff0c\u89e3\u65b9\u7a0b\u5f97x=3\u6216x=-1\uff0c\u2234\u4e0ex\u8f74\u4ea4\u70b9\u7684\u5750\u6807\u662f\uff083\uff0c0\uff09\u3001\uff08-1\uff0c0\uff09\uff1b\uff083\uff09y=x2-2x-3=\uff08x-1\uff092-4\uff0c\u5217\u8868 x -1 0 1 2 3 y 0 -3 -4 -3 0\u63cf\u70b9\u5e76\u8fde\u7ebf\uff0c\u5982\u53f3\u56fe\u6240\u793a\uff0e\uff084\uff09\u2235\u5bf9\u79f0\u8f74x=1\uff0c\u56fe\u8c61\u5f00\u53e3\u5411\u4e0a\uff0c\u2234\u5f53x\uff1e1\u65f6\uff0cy\u968fx\u589e\u5927\u800c\u589e\u5927\uff1b\uff085\uff09\u7531\u56fe\u8c61\u53ef\u77e5\uff0c\u5f53x\u2264-1\u6216x\u22653\u65f6\uff0cy\u22650\uff1b\uff086\uff09\u89c2\u5bdf\u56fe\u8c61\u77e5\uff1a-4\u2264y\uff1c12\uff0e
y=x²-2x-3
y=(x-1)²-4→对称轴x=1，顶点(1,-4)
x∈[-2，3]包含对称轴，二次项系数>0 ,开口向上
对称轴左侧单调递减：x∈[-2,1)
对称轴右侧单调递增：x∈(1,3]
∴顶点处取得最小值y=-4
最大值为两个端点值之中大的=max[y(-2),y(3)]=y(-2)=5
（1）对称轴x=1,顶点（1，-4）
（2）对称轴x=1,顶点（1，-4）
减区间[-2,1],增区间[1,3],当x=-2时，最大值5，当x=1时，最小值-4
如图
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