设函数f(x)=kx²-kx-6+k...若对于k∈[-2,2],f(x)

Question

设函数f(x)=kx²-kx-6+k ...若对于k∈[-2,2],f(x)

Answer 1

f(x)=kx2-kx-6+k=k(x-1/2)^2-6+k/2
-2<=k<=0 f(x)<0
2>=k>0 f(x)关于x=1/2对称 开口向上（y轴正向）
f(x)<0 (x-1/2)^2<6/k-1/2<=6/2-1/2=5/2
-2<=x<=3
实数x的取值范围[-2,3]