If statement with dates

I am looking to create a formula where if my date field is between certain dates then my quarter field would tag appropriately.

So if the date is between 10/01/21 - 12/31/21 then the field “Quarter” would say Quarter 4. If the date is between 1/1/22 - 4/1/22 then the field “Quarter” would say Quarter 1.

I don’t if this can be done with formulas or if there is a better way to do this but would love any help/suggestions to automate the process of manually updating my quarter field.

IF(
{Date Field},
"Quarter " & DATETIME_FORMAT({Date Field}, "Q")
)
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