The equation of a parabola is given by [tex]f(x)=a(x-h)^{2}+k [/tex] where [tex](h,k)[/tex] is the vertex.
We have the vertex is (-3,-2) so we have [tex]h=-3[/tex] and [tex]k=-2[/tex]
Substituting -3 and -2 into the [tex]f(x)[/tex]
[tex]f(x)=a(x--3)^{2}+(-2) [/tex]
[tex]f(x)=a(x+3)^{2}-2 [/tex]
Hence, the correct answer is option D
