Answer
Vertex is $(-1,9)$
x-intercepts are $(-4, 0)$ and $(2, 0)$
y-intercept is $(0,8)$
Work Step by Step
$f(x)=-x^2-2x+8$
$y=-x^2-2x+8$
$y=(x+4)(-x+2)$
$x=0$
$y=-x^2-2x+8$
$y=-(0)^2-2*0+8$
$y=-0-0+8$
$y=8$
$y=-x^2-2x+8$
$y*-1=-1*(-x^2-2x+8)$
$-y=x^2+2x-8$
$8-y=x^2+2x$
$8-y+(2/2)^2=x^2+2x+(2/2)^2$
$8-y+1^2=x^2+2x+(1)^2$
$8-y+1=x^2+2x+1$
$9-y=x^2+2x+1$
$9-y=(x+1)^2$
Vertex at $(-1,9)$
$0=(x+4)(-x+2)$
$x+4=0$
$x=-4$
$-x+2=0$
$-x=-2$
$-1*-x=-1*-2$
$x=2$
