1. **State the problem:** We are given the function $g(x) = x^2 + 6$ and need to find $g(-2)$, $g(0)$, and $g(3)$. 2. **Recall the formula:** The function is $g(x) = x^2 + 6$. To find $g(a)$ for some value $a$, substitute $x = a$ into the function. 3. **Calculate $g(-2)$:** $$g(-2) = (-2)^2 + 6 = 4 + 6 = 10$$ 4. **Calculate $g(0)$:** $$g(0) = 0^2 + 6 = 0 + 6 = 6$$ 5. **Calculate $g(3)$:** $$g(3) = 3^2 + 6 = 9 + 6 = 15$$ **Final answers:** $$g(-2) = 10, \quad g(0) = 6, \quad g(3) = 15$$