#### Answer

$b$ is divisible by $-2$ and the value of $a$

#### Work Step by Step

When finding the axis of symmetry, we use the $-b/2a$ formula.
If $b$ is divisible by -2, then (where $h = 2b$ and neither $b = 0$ nor $h=0$)
$x = -b/2a$
$x = -(-2h)/2a$
$x =2h/2a$
$x= h/a$
For $h/a$ to be an integer, $h$ must be divisible by $a$, and $a\ne0$. Thus, $b$ must be divisible by $a$, and $a\ne0$.