91Ó°ÊÓ

The axis of symmetry is given by,

$x=-\frac{b}{2a}$

Putting $a=1$and $b=6$, we get

$$\begin{gathered} x=-\frac{6}{2×1} \\ x=-\frac{6}{2} \\ x=-3 \end{gathered}$$

The equation of axis of symmetry is $x=-3$.

Vertex is a point on the line of axis of symmetry. Here axis of symmetry is $x=-3$.

We will get the vertex by putting $x=-3$in the given function,

role="math" $$\begin{gathered} f(-3)=(-3{)}^2+6(-3)+5 \\ f(-3)=9-18+5 \\ f(-3)=-4 \end{gathered}$$

Hence the vertex is $(-3,-4)$.

We get y-intercept by putting $x=0$,

role="math" $$\begin{gathered} f\left(0\right)=(0{)}^2+6(0)+5 \\ f(0)=0+0+5 \\ f(0)=5 \end{gathered}$$

Hence they-intercept is $(0,5)$.

The y-intercept $(0,5)$is $3$units to the right of axis of symmetry, so there is a points $3$units to left of symmetry.

The point is $(-6,5)$.

The $x-$intercept is given by putting the function equal to zero, so

$$\begin{gathered} x^2+6x+5=0 \\ {x}^2+5x+x+5=0 \\ (x+1)(x+5)=0 \\ x+1=0 \\ x=-1 \end{gathered}$$

or

$$\begin{gathered} x+5=0 \\ x=-5 \end{gathered}$$

So, the$x-$intercepts are $-1,-5$.

The graph is as follows,