$b$ 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 $a\ne0$.