Answer
$(10, -7)$
Work Step by Step
$h(x) =(x-10)^2-7$
For a graph in the form $f(x) = a(x-h)^2+k$, the axis of symmetry is the line $x=h$.
$h(x) =(x-10)^2-7$
Axis of symmetry
$x=10$
Vertex
$x=10$
$h(x) =(x-10)^2-7$
$h(10) =(10-10)^2-7$
$h(10) =0^2-7$
$h(10)=0-7$
$h(10)=-7$