we know that
The vertex of the function \(f(x)=x^{2}\) is the point \((0,0)\)
The vertex of the function \(f(x)=(x-h)^{2}+k\) is the point \((4,-2)\)
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 \(4\)
the value of k is \(-2\)
the equation is
\(f(x)=(x-4)^{2}-2\)
therefore
the answer is the option a
\(4\)
