Step 1: Place the test in its trimester; the quad test is a hallmark of second-trimester serum screening.
Step 2: Its optimal window is $15$ to $20$ weeks, when the four analytes give the most accurate risk estimate for Down syndrome and open neural tube defects.
Step 3: Earlier ranges ($8$ to $12$ and $11$ to $15$ weeks) are first-trimester territory, and $18$ to $22$ weeks runs past the ideal point. The $15$ to $20$ week band fits best.
\[\boxed{\text{15 to 20 weeks}}\]