Where is the SP 2010 out of the box workflow status value stored?

Question

I created an out of the box Approval - SharePoint 2010 workflow (TEST1) on a custom list. When I created this out of the box workflow, I specified a name for the task (TEST1 Tasks) and history (TEST1 History) list. 
The workflow is creating tasks, sending emails, and the task emails lead me to a screen where I can approve or reject the requests.
However, TEST1 - the list that contains the items created - doesn't have a status column.  The TEST1 Tasks has a status column. But I would prefer the people working with the workflow just look at TEST1 and not the Tasks or History lists.
What is the preferred way to create one of these list workflows so that the admins only have to look at the specific tasks that have been submitted and they can see which have been approved or not?
Thank you
 

Answer 1

Thank you for your reply. Initially, I didn't have content approval turned on, had workflow approval turned on, but didn't have a status column. I also had an error in the history list that the status could not be created.
When I turned on the content approval, then I got a status column, but now my list has a warning across the top telling the user that their request won't be public until approved.
I don't really WANT a document approval workflow. But I don't see how to set up what I do want.
What I need is a simple custom list - a few lookup columns, the rest static data columns, that describe an action that is being requested. That request (ala the list item) is what needs to be approved or rejected. There is no publishing needed in this workflow.
The approval workflow was the closest I could see for setting up such a simple request workflow.