y-intercept -> x=0
[tex]\begin{gathered} y=-0^2-6\cdot0-8 \\ y=-0-0-8 \\ y=-8 \end{gathered}[/tex]y-intercept -> x=0, then: (0,-8)
x-intercept -> y=0
[tex]\begin{gathered} y=-x^2-6x-8 \\ \Delta=36-32=4 \\ x=\frac{6\pm\sqrt[]{4}}{-2}=\frac{6\pm2}{-2} \\ x_1=\frac{8}{-2}=-4 \\ x_2=\frac{4}{-2}=-2_{} \end{gathered}[/tex]x-intercept -> y=0, then: (-2,0) e (-4,0)
vertex
[tex]x_v=-\frac{b}{2a}=-\frac{6}{-2}=-3[/tex]now find yv
[tex]\begin{gathered} y_v=-(-3)^2-6\cdot(-3)-8 \\ y_v=-9+18-8=9-8=1 \end{gathered}[/tex]vertex= (-3,1)
The graph below shows the x-intercept and y-intercept
