Step-by-step explanation:
[tex]y=x^2+11x+24[/tex]
To graph the above equation , we need to find out the x intercepts
Replace y with 0 and solve for x
[tex]0=x^2+11x+24[/tex]
[tex]=(x+8)(x+3)[/tex]
Set the factors =0 and solve for x
x+8=0 so x=-8
x+3=0 so x=-3
X intercepts are (-8,0) and (-3,0)
Now we find out vertex, we apply formula x=-b/2a
We know a=1 , b= 11
[tex]x=\frac{-b}{2a} =\frac{-11}{2(1)} = -5.5[/tex]
Now we plug in x=-5.5 and find out y
[tex]y=x^2+11x+24[/tex]
[tex]y=(-5.5)^2+11(-5.5)+24= -6.25[/tex]
So vertex is (-5.5,-6.25)
We got x intercepts and vertex, the graph is attached below
