Answer
5, -5
Work Step by Step
The two numbers are $x$ and $x-10$. The product is $(x)(x-10)$, and we want this to be as small as possible. This product is as small as possible as the vertex.
$x(x-10)$
$x^2-10x=y$
$x^2-10x+(-10/2)^2=y+(-10/2)^2$
$x^2-10x+(-5)^2=y+(-5)^2$
$x^2-10x+25=y+25$
$(x-5)^2=y+25$
$(x-5)^2-25=y+25-25$
$(x-5)^2-25=y$
Vertex: $(5, -25)$
$x-10$
$5-10$
$-5$
The numbers are 5, -5.
