Question

求值域。。

Y= -(T- (A/2))^2 + (A/4)-1 T的范围是[跟号2/2,1] A∈R

Answer 1

Y= -(T- (A/2))^2 + (A/4)-1
=-A^2/4+AT/2-T^2+A/4-1
=(-1/4)[A^2+A(2T+1)]-T^2-1
=(-1/4)[A+(2T+1)/2]^2+T-3/4,
T∈[(√2）/2,1], A∈R ,
∴Y的取值范围是(-∞，1/4].