Answer
The function has a minimum value of $-6$.
Work Step by Step
The given function is
$\Rightarrow y=x^2-4x-2$
Add $6$ to each side.
$\Rightarrow y+6=x^2-4x-2+6$
Simplify.
$\Rightarrow y+6=x^2-4x+4$
Write the right side as the square of a binomial.
$\Rightarrow y+6=(x-2)^2$
Write in vertex form.
$\Rightarrow y=(x-2)^2-6$
The vertex is $(2,-6)$. Because $a$ is positive $(a=1)$, the parabola opens up and the $y-$coordinate of the vertex is the minimum value.
Hence, the function has a minimum value of $-6$.
