Answer
The function has a minimum value of $-3$.
Work Step by Step
The given function is
$\Rightarrow y=x^2-2x-2$
Add $3$ to each side.
$\Rightarrow y+3=x^2-2x-2+3$
Simplify.
$\Rightarrow y+3=x^2-2x+1$
Write the right side as the square of a binomial.
$\Rightarrow y+3=(x-1)^2$
Write in vertex form.
$\Rightarrow y=(x-1)^2-3$
The vertex is $(1,-3)$. 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 $-3$.
