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 2)抛物线与x轴两个交点间的距离为四倍根号三3)抛物线的顶点在直线y=2x+1上4)抛物线与y轴交点的纵坐标为-
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![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 2)抛物线与x轴两个交点间的距离为四倍根号三3)抛物线的顶点在直线y=2x+1上4)抛物线与y轴交点的纵坐标为-](/uploads/image/z/6798260-20-0.jpg?t=%E5%B7%B2%E7%9F%A5%E6%8A%9B%E7%89%A9%E7%BA%BFy%3Dx%5E2%2Bmx%2B2m-m%5E2%2C%E6%A0%B9%E6%8D%AE%E4%BB%A5%E4%B8%8B%E6%9D%A1%E4%BB%B6%2C%E5%88%86%E5%88%AB%E6%B1%82%E5%87%BA%E7%9B%B8%E5%BA%94%E7%9A%84m%E5%80%BC1%EF%BC%89%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA-1+2%EF%BC%89%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8Ex%E8%BD%B4%E4%B8%A4%E4%B8%AA%E4%BA%A4%E7%82%B9%E9%97%B4%E7%9A%84%E8%B7%9D%E7%A6%BB%E4%B8%BA%E5%9B%9B%E5%80%8D%E6%A0%B9%E5%8F%B7%E4%B8%893%EF%BC%89%E6%8A%9B%E7%89%A9%E7%BA%BF%E7%9A%84%E9%A1%B6%E7%82%B9%E5%9C%A8%E7%9B%B4%E7%BA%BFy%3D2x%2B1%E4%B8%8A4%EF%BC%89%E6%8A%9B%E7%89%A9%E7%BA%BF%E4%B8%8Ey%E8%BD%B4%E4%BA%A4%E7%82%B9%E7%9A%84%E7%BA%B5%E5%9D%90%E6%A0%87%E4%B8%BA-)
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 2)抛物线与x轴两个交点间的距离为四倍根号三3)抛物线的顶点在直线y=2x+1上4)抛物线与y轴交点的纵坐标为-
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
2)抛物线与x轴两个交点间的距离为四倍根号三
3)抛物线的顶点在直线y=2x+1上
4)抛物线与y轴交点的纵坐标为-3
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 2)抛物线与x轴两个交点间的距离为四倍根号三3)抛物线的顶点在直线y=2x+1上4)抛物线与y轴交点的纵坐标为-
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
抛物线改写为:y=(x+m/2)^2-5/4*m^2+2m,则顶点为(-m/2,-5/4*m^2+2m)
1)当x=-m/2时,y取最小值,即(-m/2+m/2)^2-5/4*m^2+2m=-1,得方程:5m^2-8m-4=0,解得:m1=-2/5、m2=2;
2)当y=0时,x1=-m/2+1/2*√(5m^2-8m),x2=-m/2-1/2*√(5m^2-8m),x1-x2=√...
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抛物线改写为:y=(x+m/2)^2-5/4*m^2+2m,则顶点为(-m/2,-5/4*m^2+2m)
1)当x=-m/2时,y取最小值,即(-m/2+m/2)^2-5/4*m^2+2m=-1,得方程:5m^2-8m-4=0,解得:m1=-2/5、m2=2;
2)当y=0时,x1=-m/2+1/2*√(5m^2-8m),x2=-m/2-1/2*√(5m^2-8m),x1-x2=√(5m^2-8m)=4√3,得方程5m^2-8m-48=0,解得:m1=-12/5、m2=4;
3)令2(-m/2)+1=-5/4*m^2+2m,得方程5m^2-12m+4=0,解得:m1=2/5、m2=2;
4)令x=0,即2m-m^2=-3,得方程m^2-2m-3=0,解得:m1=-1、m2=3。
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