1. The problem asks to find the function $g(x)$ which is the translation 9 units up of the function $f(x) = x^2$. 2. The general form for a vertical translation of a function $f(x)$ by $k$ units up is: $$g(x) = f(x) + k$$ 3. Since $f(x) = x^2$ and the translation is 9 units up, we have: $$g(x) = x^2 + 9$$ 4. Writing $g(x)$ in the form $a(x - h)^2 + k$, where $a$, $h$, and $k$ are integers: - Here, $a = 1$ (coefficient of $x^2$), - $h = 0$ (no horizontal shift), - $k = 9$ (vertical shift up by 9). 5. Therefore, the function is: $$g(x) = 1(x - 0)^2 + 9$$ This is the required translation of $f(x)$ 9 units up.