Answer
$a$ has unit $m^{-1}$.
$b$ is dimensionless.
$c$ has unit $m$.
Work Step by Step
For the equation $y=ax^2+bx+c$,
LHS has $y$ with SI unit $m$.
In RHS, to ensure correct unit analysis, all components must have Si unit $m$.
$x^2$ has SI unit $m^2$. Thus, $a$ has unit $m/m^2$ = $m^{-1}$.
$bx$ has SI unit $m$. Thus, $b$ is dimensionless.
$c$ has SI unit $m$.
