Given the function [tex] g(x)=2x^2+12x+21 [/tex]. The above function can be written as
[tex] g(x)=2x^2+12x+21 \\
g(x)=2(x^2+6x)+21 \\
g(x)=2(x^2+6x+9-9)+21 \\
g(x)=2(x^2+6x+9)-18+21 \\
g(x)=2(x+3)^2+3 [/tex]
a)Now, the function [tex] g(x)=2(x+3)^2+3 [/tex] has minimum value since the coefficient of [tex] (x+3)^2 [/tex] is [tex] 2>0 [/tex].
b) The minimum value of the function occurs at [tex] x=-3 [/tex] and its value is
[tex] g(-3)=3(-3+3)^2+3 =3 [/tex]
c)The minimum value of the function occurs at [tex] x=-3 [/tex].
