Employeee fills out then submit to supervisor then to HR

I have a question, I have a need for a vacation request form, were the employee fills out the initial form with name dates and supervisor and notes/reason and then submits the form to the supervisor to complete by approving/denying the request and signing it, and submits to HR.

Is this possible?

That's possible. Please check this guide to learn how to set up the approval process workflow. 

https://www.jotform.com/help/432-A-General-Approach-on-Building-an-Approval-Process-Workflow