I am claiming a dependent that is an adult. Wouldn't that qualify me as "Head of Household"?

[ee-ea]

Maybe   See this info    https://turbotax.intuit.com/tax-tips/family/guide-to-filing-taxes-as-head-of-household/L4Nx6DYu9

[MarilynG1]

To claim another adult (not related to you) as a Dependent, they must have have lived with you all year.  Their income must be under $4,400, and you must have provided over half of their support.  This means you paid over half of rent, utilities, etc. and that they are in your name.  Be sure you can document that you paid over half the household expenses. 

They also cannot be married, or claimed as a dependent on someone else's return. 

If these apply, you can file as Head of Household with a Qualifying Dependent.