By expressing $x^2-10x-2$ in the form $(x-h)^2+k$, where $h$ and $k$ are constants, write down the coordinates of the minimum point of the graph of $y = x^2-10x-2$. Answer (... , ...)

1. Complete the square for the quadratic expression.

$x^2-10x-2=(x-5)^2-25-2=(x-5)^2-27$

2. Use vertex form to identify the minimum point.

Since $y=(x-5)^2-27$ and $(x-5)^2\geq 0$, the minimum value occurs when $x=5$. Hence the minimum value of $y$ is $-27$.