(1)抛物线y=ax的平方+bx+c的顶点坐标为(2,4)
-b/2a=2
b=-4a
y(2)=4a+2b+c=4
c=4+4a
(2)S三角形ODE：S三角形OEF=1：3
DE:EF=1:3
xE:xF=1:4
y=ax^2-4ax+4+4a
y=kx+4
ax^2-(4a+k)x+4a=0
xExF=4
xE=1,xF=4或
xE=-1,xF=-4
xE+xF=5或xE+xF=-5
4+k/a=5或4+k/a=-5
k=a或k=-9a
判别式=8ak+k^2>0
(3)
m^2=(xE-xF)^2+(yE-yF)^2=(xE-xF)^2+k^2*(xE-xF)^2=(k^2+1)[(xE+xF)^2-4xE*xF]=
=(k^2+1)(25-16)= 9(k^2+1)∈(18,45)
(k^2+1)∈(2,5)
[1]
k=a
a^2∈(1,4)
a∈(-2,-1)∪(1,2)
[2]
k=-9a
81a^2∈(1,4)
a∈(-2/9,-1/9)∪(1/9,2/9)
故a∈(-2,-1)∪(-2/9,-1/9)∪(1/9,2/9)∪(1,2)