Answer
4, -4
Work Step by Step
The two numbers are $x$ and $x-8$. The product is $(x)(x-8)$, and we want this to be as small as possible. This product is as small as possible as the vertex.
$x(x-8)$
$x^2-8x=y$
$x^2-8x+(-8/2)^2=y+(-8/2)^2$
$x^2-8x+(-4)^2=y+(-4)^2$
$x^2-8x+16=y+16$
$(x-4)^2=y+16$
$(x-4)^2-16=y+16-16$
$(x-4)^2-16=y$
Vertex: $(4, -16)$
$x-8$
$4-8$
$-4$
The numbers are 4, -4.
