Answer
The axis of symmetry is $x=-3$.
The vertex is $(-3,-4)$.
Work Step by Step
The given function is
$g(x)=x^2+6x+5$
It is in the form of $f(x)=ax^2+bx+c$
We have $a=1,b=6$ and $c=5$
(a)
Equation for the axis of symmetry.
$\Rightarrow x=-\frac{b}{2a}$
Substitute $1$ for $a$ and $6$ for $b$.
$\Rightarrow x=-\frac{6}{2(1)}$
Simplify.
$\Rightarrow x=-\frac{3}{1}$
$\Rightarrow x=-3$
The axis of symmetry is $x=-3$.
(b)
Substitute $-3$ for $x$ in the given function.
$\Rightarrow g(-3)=(-3)^2+6(-3)+5$
Simplify.
$\Rightarrow g(-3)=9-18+5$
$\Rightarrow g(-3)=14-18$
$\Rightarrow g(-3)=-4$
The vertex is $(-3,-4)$.
