已知抛物线y=2x平方-6x+5用配方法把它化为y=a(x-h)平方+K的形式,并指出它的开口方向,对称轴和顶点坐标

\u5df2\u77e5\u629b\u7269\u7ebfY=\u8d1f1/2X\u5e73\u65b9+\uff085-M\uff09X+M-3\u7684\u5bf9\u79f0\u8f74\u662fY\u8f74\u6c42\u629b\u7269\u7ebf\u7684\u9876\u70b9\u5750\u6807

y=-1/2x²+\uff085-m\uff09x+m-3
a=-1/2 b=5-m c=m-3
\u5f53x=-b/2a=-\uff085-m\uff09/-1 =5-m
y=4ac-b²/4a=4*\uff08-1/2\uff09*\uff08m-3\uff09-\uff085-m\uff09²/4*\uff08-1/2\uff09=-2\uff08m-3\uff09-\uff085-m\uff09²/\uff08-2\uff09
\uff08x\uff0cy\uff09\u4e3a\u30105-m \uff0c-2\uff08m-3\uff09-\uff085-m\uff09²/\uff08-2\uff09\u3011
\u2235\u5b83\u7684\u5bf9\u79f0\u8f74\u662fy\u8f74 \u2234\u5b83\u7684\u4e00\u6b21\u9879\u7cfb\u6570\u4e3a0 \u2234m=5
\u2234\uff08x\uff0cy\uff09\u4e3a\uff080 \uff0c2\uff09
\u8fd9\u4e2a\u51fd\u6570\u7684\u89e3\u6790\u5f0f\u4e3ay=-1/2x²+2

\u629b\u7269\u7ebfy=-2x²+6x-1\u7684\u9876\u70b9\u5750\u6807\u4e3a\uff1f\u5bf9\u79f0\u8f74\u4e3a\uff1f
\u89e3\uff1ay=-2(x²-3x)-1=-2[(x-3/2)²-9/4]-1=-2(x-3/2)²+9/2-1=-2(x-3/2)²+7/2
\u6545\u9876\u70b9\u5750\u6807\u4e3a(-3/2\uff0c7/2)\uff1b\u5bf9\u79f0\u8f74\uff1ax=3/2.

y=2x^2-6x+5=2[(x-1.5)^2+0.25]=2(x-1.5)^2+0.5
开口向上
对称轴x=3/2
顶点坐标(3/2,0.5)

解:y=2x²-6x+5=2(x²-3x)+5=2[(x-3/2)²-9/4]+5=2(x-3/2)²-9/2+5=2(x-3/2)²+1/2
开口朝上;对称轴x=3/2;顶点(3/2,1/2).

y=2x平方-6x+5=2(x-3/2)^2+1/2
开口方向向上
对称轴x=3/2
顶点坐标(3/2,1/2)

y=2(x-3/2)^2 + 1/2, 开口向上,对称轴:x=3/2,顶点坐标:(3/2,1/2)

y=2(x-2/3)平方+1/2
开口方向向上
对称轴 x=3/2
定点坐标 (3/2,1/2)

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