How do i solve and graph y=x^2+5x+6

To graph this equation we find x intercepts and vertex

To find x intercept we replace y with 0

Factor the right hand side

0 = (x+3)(x+2)

x+3 =0  and x+2 =0

x=-3  and x=-3

So x intercept are (-3,0) and (-2,0)

Now we find vertex, vertex formula is x =

, a= 1 and b = 5

so x= = -2.5

Now plug in -2.5 in

= -0.25

So vertex is (-2.5, -0.25)

The value of a=1 that is positive , so parabola opens upwards.

The graph is attached below.