[tex]y=x^2+5x+6[/tex]
To graph this equation we find x intercepts and vertex
To find x intercept we replace y with 0
[tex]0=x^2+5x+6[/tex]
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 = [tex]\frac{-b}{2a}[/tex]
[tex]y=x^2+5x+6[/tex] , a= 1 and b = 5
so x= [tex]\frac{-5}{2(1)}[/tex]= -2.5
Now plug in -2.5 in [tex]y=x^2+5x+6[/tex]
[tex]y=(-2.5)^2+5(-2.5)+6[/tex]= -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.
