若函数f(x)=x^2-4ax+2a+6的值为非负值,求函数f(a)=2-a|a+3|的值域
问题描述：
若函数f(x)=x^2-4ax+2a+6的值为非负值,求函数f(a)=2-a|a+3|的值域
答
估计题意可知x^2-4ax+2a+6≥0恒成立
则△=16a²-4(2a+6)≤0
2a²-a-3≤0
=> -1≤a≤3/2
f(a)=2-a|a+3|
则因-1≤a≤3/2,则a+3>0
f(a)=2-a(a+3)
=-(a+3/2)²+17/4 ( -1≤a≤3/2)
f(a)min=f(3/2)=-19/4,f(a)max=f(-1)=4
f(a)∈[-19/4,4]