f(x)=-x^2-4x+1 (-3

来源：学生作业帮助网编辑：作业帮时间：2024/10/30 10:23:24

f(x)=-x^2-4x+1 (-3
f(x)=-x^2-4x+1 (-3

f(x)=-x^2-4x+1 (-3
f(x)=-x^2-4x+1=-(x^2+4x+4)+5=-(x+2)^2+5.
对称轴x=-2,在所给的定义域内,又因为函数开口向下,所以此处为最大值,即：
f(x)max=f(-2)=5;
进一步知道最小值为：
f(x)min=f(3)=-5^2+5=-20
所以函数的值域为[-20,5].

x)=-x^2-4x+1 (-3<=x<=3)的值域
对称轴 = - (-4) / ( -2) = -2
当x =3 时最小 = -9-12 +1 = -20
当x= -2 时最大 = -4 + 8 +1 = 5
值域为 [ -20 , 5 ]

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