  In this paper, we study Diophantine exponents $w_n$ and $w_n ^{*}$ for
Laurent series over a finite field. Especially, we deal with the case $n=2$,
that is, quadratic approximation. We first show that the range of the function
$w_2-w_2 ^{*}$ is exactly the closed interval $[0,1]$. Next, we estimate an
upper bound of the exponent $w_2$ of continued fractions with low complexity
partial quotients.
