已知二次函数y=ax^2+bx+c图像与y轴交于A,与反比例函数y=2⼀x的图像有两个公共点D、E，点D、E

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对于y=ax^2+bx=2 令x=0，则y=2 ∴A(0,2)

对于y=2/x 令y=2 则x=1 ∴D（1，2）

令x=2 则y=1 ∴E（2，1）

∵D（1，2）E(2,1)在y=ax^2+bx+2上

∴a=-1/2 b=1/2

∴y=-1/2x^2+1/2x+2

=-1/2(x-1/2)^2+15/8

顶点坐标为（1/2，15/8)

此题错误
设D（2/c，c），E（c，2/c），则有2/c＝a*c2＋bc＋c，c＝a*（2/c）2＋b*（2/c）＋c，故有2/c－c＝a*（c－2/c）（c＋2/c）＋b*（c－2/c），c－2/c＝0或a（c＋2/c）＋b＝－1，即c＝±2^1/2（舍去），又有2a/c＋b＝0，故ac＝－1，从而有a＝－1/c，b＝2/c^2，c＞2^1/2，从而A（0，c），D（2/c，c），E（c，2/c），c＞2^1/2。
此题的答案是不确定的。

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