Use What-If parameter for selecting a date interval

A calculated column won't work as it is only calculated during data refresh, it does not take into account any filters or slicers so won't update when your user changes the what if parameter.

You could create a calculation group with a single calculation item, something like

Filtered days calculation =
VAR numDays = SELECTEDVALUE ( 'What if parameter'[Num days] )
VAR baseDate = TODAY ()
VAR startDate = baseDate - numDays
VAR endDate = baseDate + numDays
RETURN
    CALCULATE (
        SELECTEDMEASURE (),
        DATESBETWEEN ( 'Date'[Date], startDate, endDate )
    )

then apply that as a filter to the visuals which you want to be filtered