we have
[tex]g(x)=4-x^{2}[/tex]
the vertex of the function g(x) is the point [tex](0,4)[/tex]
the vertex of the function f(x) is the point [tex](0,0)[/tex]
so
the rule of the translation of g(x) to f(x) is
(x,y)------> (x,y-4)
that means
the translation is [tex]4[/tex] units down
therefore
the equation of the function f(x) is
[tex]f(x)=g(x)-4\\f(x)=(4- x^{2})-4 \\f(x)=- x^{2}[/tex]
therefore
the answer is
[tex]f(x)=- x^{2}[/tex]
