The graph of f(x)=x^2 is sketched in red and the graph of g(x) is sketched in blue. Use the translation rule and f(x)=x^2 to identify the function g(x).
We can use the vertex form of a quadratic, [tex]y = a(x-h)^{2} + k[/tex], to find that [tex]g(x) = a x^{2} - 7[/tex]. Plugging [tex](x,y)[/tex] ordered pairs into g(x), we see that a = 1. For example, for [tex](3, 2)[/tex], [tex]2 = a * 3^{2} - 7[/tex]. Solving for a gives 1.