1. **State the problem:** We are given the function $g(x) = x^2 + 6$ and need to find $g(0)$, $g(-2)$, and $g(\sqrt{3})$. 2. **Recall the formula:** The function is $g(x) = x^2 + 6$. To find $g(a)$ for some value $a$, substitute $x$ with $a$ and simplify. 3. **Calculate $g(0)$:** $$g(0) = 0^2 + 6 = 0 + 6 = 6$$ 4. **Calculate $g(-2)$:** $$g(-2) = (-2)^2 + 6 = 4 + 6 = 10$$ 5. **Calculate $g(\sqrt{3})$:** $$g(\sqrt{3}) = (\sqrt{3})^2 + 6 = 3 + 6 = 9$$ **Final answers:** - $g(0) = 6$ - $g(-2) = 10$ - $g(\sqrt{3}) = 9$