Answer
The function has a minimum, and the value of that minimum is $y=7$.
Work Step by Step
The $A$-value is positive, so the function will open upwards. Therefore, the function will have a minimum.
The $x$-value of the minimum's coordinate is not really useful in the answer, but we still need to find it to calculate the $y$-value of the minimum. The $x$-value of the coordinate of the function's minimum is $x=-\frac{b}{2a}$, where the function is in the form $x=Ax^{2}+Bx+C$.
Thus, the value of $B$ is $8$, and the value of $A$ is $2$. Therefore:
$x=-\frac{8}{2\times2}=-\frac{8}{4}=-4$
Now we can plug that $x$-value into the function, and evaluate for $y$.
$y=2\times(-4)^{2}+8\times(-4)+7=32+(-32)+7=7$
Therefore, the $y$-value is $7$.
