This article illustrates how to retrieve SQL Server database backups information, depending upon what exactly you are looking for, this article will help you to locate desired information. Below are few scenarios.
Above statement will provide you all the databases backup history, this is going to be our master table to retrieve various type of information about database backups.
select database_name, backup_start_date,backup_finish_date from msdb.dbo.backupset
select count(1) from msdb.dbo.backupset where database_name='Your_db_name'
group by database_name