Answer
The function has a minimum value of $4$
Work Step by Step
The given function is
$\Rightarrow y=x^2+12x+40$
Subtract $4$ from each side.
$\Rightarrow y-4=x^2+12x+40-4$
Simplify.
$\Rightarrow y-4=x^2+12x+36$
Write the right side as the square of a binomial.
$\Rightarrow y-4=(x+6)^2$
Write in vertex form.
$\Rightarrow y=(x+6)^2+4$
The vertex is $(-6,4)$. 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 $4$
