Quadratic probing maximum load factor with $c_1 = c_2 = 0.5$ to guarantee successful insertion
For the case you describe ($c_1=c_2=1/2$, $m=2^k$), you can reach a load factor of 1. The probe sequence touches all the cells in the table.

As a practical matter, you probably don't want to get really close to a load factor of 1, as the probing can take $O(n)$ time.