we know that
The graph of g(x) is a translation of the function f(x)
so
\(f(x)=x^{2}\)
the vertex of f(x) is the point \((0,0)\)
the vertex of g(x) is located \(5\) units above and \(7\) units to the right of the vertex of f(x)
The rule of the translation is
\((x,y)--------> (x+7,y+5)\)
Find the vertex of the function g(x)
\((0+7,0+5)=(7,5)\)
the vertex of g(x) is the point \((7,5)\)
the equation of the function g(x) in the vertex form is equal to
\(g(x)=(x-h)^{2} +k\)
where
(h,k) is the vertex
substitute the value of the vertex in the equation
\(g(x)=(x-7)^{2} +5\)
the answer is
\(g(x)=(x-7)^{2}+5\)
