已知抛物线y=x^2+mx+2m-m^2,根据以下条件,分别求出相应的m值
1）抛物线的最小值为-1
y=x^2+mx+2m-m^2
=x^2+mx+m^2/4-m^2/4+2m-m^2
=(x+m/2)^2-5m^2/4+2m
-5m^2/4+2m=-1
5m^2-8m-4=0
(5m+2)(m-2)=0
m=-2/5 m=2
2）抛物线与x轴两个交点间的距离为四倍根号三
x1=(-m+(m^2-4(2m-m^2))^0.5/2
x2=(-m-(m^2-4(2m-m^2))^0.5/2
x1-x2=4√3
(m^2-4(2m-m^2))^0.5=4√3
m^2-4(2m-m^2)=48
m^2-8m+4m^2=48
5m^2-8m-48=0
(5m+12)(m-4)=0
m=-12/5 m=4
3）抛物线的顶点在直线y=2x+1上
y=(x+m/2)^2-5m^2/4+2m
-5m^2/4+2m=-2*m/2+1
5m^2-12m+4=0
(5m-2)(m-2)=0
m=2/5 m=2
4）抛物线与y轴交点的纵坐标为-3
y=x^2+mx+2m-m^2
-3=2m-m^2
m^2-2m-3=0
(m-3)(m+1)=0
m=3 m=-1