Crabgrass seed must have light to germinate, and a high mowing height will help shade the soil. Also, root depth and mowing height are related on upright growing grasses such as tall fescue and Kentucky bluegrass — the higher the height of cut, the deeper the root system. A deeper root system means a more drought-resistant turf.
So, how low should you go on the first cutting? On tall fescue and Kentucky bluegrass, you can mow as low as 1 to 1½ inches. Be careful you don't go so low that you scalp the turf. After that, raise the mowing height for Kentucky bluegrass to 2 to 3 inches but 3 to 3½ inches for tall fescue. (Ward Upham)