You can do this by combining two functions - dateadd and datetrunc.
Using dateadd - we can find out the date three months ago (i.e. within last quarter)
Using datetrunc - we can truncate/round-down a date to giving the start of the period, in our case the start of the quarter. The format for that would be:
If you combine these - by passing the 'last quarter' date into datetrunc, you get:
Just to add to what Alyn suggested, there are times when people want to know the LAST day of a quarter or a month.
You can do the same thing Alyn did, but position yourself to the first day of the NEXT quarter (or month) and then simply subtract 1 from that.
In your case you would only need to DATETRUNC to the current quarter, and then subtract 1.
That would give you the last day of the prior quarter.
DATEADD('month', 1, DATETRUNC('month',[Date Field]))-1
That would give you the last day of the current month. (Truncate to the beginning of this month. Add a month. Subtract a day.) Tableau date math is robust enough to get the right last day (30, 31, 28 or 29) based on what month is it and leap years and all.