we have
[tex]f(x)=x^{2}[/tex]
The vertex of f(x) is the point [tex](0,0)[/tex]
The vertex of g(x) is the point [tex](-4,-3)[/tex] ----> see the graph
So
The rule of the translation is
[tex]f(x)------> g(x)[/tex]
[tex](x,y)-----> (x-4,y-3)[/tex]
that means
the translation is [tex]4[/tex] units to the left and [tex]3[/tex] units down
The equation of the function g(x) in the vertex form is equal to
[tex]g(x)=(x-h)^{2} +k[/tex]
where
(h,k) is the vertex
[tex](h,k)=(-4,-3)[/tex]
Substitute
[tex]g(x)=(x+4)^{2} -3[/tex]
therefore
the answer is the option C
[tex]g(x)=(x+4)^{2} -3[/tex]
