Question

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).

Answer 1

We can use the vertex form of a quadratic, $y = a(x-h)^{2} + k$, to find that $g(x) = a x^{2} - 7$. Plugging $(x,y)$ ordered pairs into g(x), we see that a = 1. For example, for $(3, 2)$, $2 = a * 3^{2} - 7$. Solving for a gives 1.