Answer
$$
y=x^{2}+5x+6
$$
The $x$-intercepts are $-2 , -3 $.
The $y$-intercept is 6.
Vertex parabola is $\left(-\frac{5}{2} , -\frac{1}{4}\right)$.
The axis is $x=-\frac{5}{2}$ , the vertical line through the vertex.
Plotting the vertex, the $y$-intercept,the $x$-intercepts. and the point $\left(-\frac{5}{2} , -\frac{1}{4}\right)$ gives the graph in Figure
Work Step by Step
$$
y=x^{2}+5x+6
$$
The $x$-intercepts can be found by letting $y=0$ to get
$$
y=x^{2}+5x+6=(x+2)(x+3)=0
$$
from which $x=-2 $ and $x=-3 $ are the $x$-intercepts.
Set $x=0 $ to find the $y$-intercept.
$$
y=(0)^{2}+5(0)+6=6.
$$
So the $y$-intercept is 6.
The $x$-coordinate of the vertex is :
$$
x=\frac{-b}{2a}=\frac{-5}{2}
$$
Substituting this into the equation gives
$$
y=\left(-\frac{5}{2}\right)^{2}+5\left(-\frac{5}{2}\right)+6=\frac{25}{4}-\frac{25}{2}+6=-\frac{1}{4}
$$
The vertex is $\left(-\frac{5}{2} , -\frac{1}{4}\right)$.
The axis is $x=-\frac{5}{2}$ , the vertical line through the vertex.
Plotting the vertex, the $y$-intercept,the $x$-intercepts. and the point $\left(-\frac{5}{2} , -\frac{1}{4}\right)$ gives the graph in Figure