Use the simplest script to find the latest database backup and the location.

SELECT b.server_name ,b.database_name,b.user_name, f.physical_device_name,
b.backup_finish_date,b.backup_size /1024/1024 AS size_MB,b.type,b.recovery_model,
b.has_bulk_logged_data,b.is_copy_only,f.mirror
FROM MSDB.DBO.BACKUPMEDIAFAMILY F
JOIN MSDB.DBO.BACKUPSET B
ON (f.media_set_id=b.media_set_id)
WHERE database_name='test'
--AND B.type='L'
ORDER BY b.backup_finish_date DESC

You can add more conditions on where clause http://msdn.microsoft.com/en-us/library/ms186299.aspx.

Like backup Type

D = Full

I = Differential database

L = Log

F = File or filegroup

G =Differential file

P = Partial

Q = Differential partial