I am a row crop agronomist by trade, working in South Georgia. Grasses are not my specialty at all, but I know that their fertility requirements vary a lot from species to species, climate to climate, and depending on soil type.
Most grasses respond to nitrogen, with a decent amount of the total being available in the nitrate form. Depending, again, on soil type and species, sulfur as a secondary element may trigger a good greening effect when used to complement nitrogen. In our sandy soils, we need magnesium as well, but in many areas that element is not needed. Just about any of them benefit from minor elements of iron, zinc, and sometimes boron and copper.
If your soils are naturally acidic, lime may be necessary to bring up pH. Most grasses are not heavy users of phosphorus, but some are, and it is the element that more than any, promotes good root development. Light doses of potassium usually help maintain healthier growth, the main nutrient plants need to stand well and ward off disease pressure.
Bermudas are the heaviest users of all of the above, regardless of where they may be grown.
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