we know that
The vertex of the function [tex]f(x)=x^{2}[/tex] is the point [tex](0,0)[/tex]
The vertex of the function [tex]f(x)=(x-h)^{2}+k[/tex] is the point [tex](4,-2)[/tex]
The x-coordinate of the vertex is equal to h
the y-coordinate of the vertex is equal to k
so
the value of h is [tex]4[/tex]
the value of k is [tex]-2[/tex]
the equation is
[tex]f(x)=(x-4)^{2}-2[/tex]
therefore
the answer is the option a
[tex]4[/tex]
