The given equation is:
[tex]y=x^2+5x+6[/tex]
To find the x-intercepts, let y = 0
[tex]\begin{gathered} x^2+5x_{}+6=0 \\ x^2+2x+3x+6=0 \\ x(x+2)+3(x+2)=0 \\ (x+2)(x+3)=0 \\ x+2=0 \\ x=-2 \\ x+3=0 \\ x=-3 \end{gathered}[/tex]
The x-intercepts are (-3, 0) and (-2, 0)
The graph of the equation is plotted below
