A2. For which values of the parameter $a \in \mathbb{R}$ is the function $f(x)=\log \left(x^{2}+(a+4) x+9\right)$ defined on the set of all real numbers?
(A) $a-10$
(C) $-2<a<10$
(D) $-10<a<2$
(E) $a=-4$
A2. We find that the domain of the given function $f$ will be the set of all real numbers provided that $x^{2}+(a+4) x+9>0$. This will be satisfied if $D<0$. Simplify the left side of the inequality:

$$
D=b^{2}-4 a c=(a+4)^{2}-4 \cdot 1 \cdot 9=a^{2}+8 a-20=(a+10)(a-2)
$$

Solve the quadratic inequality $(a+10)(a-2)<0$. The solutions to the quadratic equation $(a+10)(a-2)=0$ are $a_{1}=-10$ and $a_{2}=2$. The solution to the quadratic inequality corresponds to the interval $-10<a<2$. The correct answer is D.