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There are tax benefits to claiming parents as dependents and as qualifying you for Head of Household filing status, but you can only claim your parents as dependents if you meet the test for a qualifying relative per Table 5 from IRS Publication 501 at this link. The gross income test and support test must be met. They also cannot have already filed a joint return for this year claiming their own standard deduction.

To meet the gross income test, each dependent's gross income for the year must be less than $4,400. Gross income is all income in the form of money, property, and services that isn't exempt from tax, including all taxable unemployment compensation, taxable social security benefits, and certain amounts received as scholarship and fellowship grants. 

To meet the support test, you must generally provide more than half of each person's total support during the calendar year. You figure whether you have provided more than half of a person's total support by comparing the amount you contributed to that person's support with the entire amount of support that person received from all sources. This includes support the person provided from the person’s own funds.

You may be able to file as head of household if you meet all the following requirements:

• You are unmarried or considered unmarried on the last day of the year. See Marital Status, earlier, and Considered Unmarried, later.
• You paid more than half the cost of keeping up a home for the year.
• A qualifying person lived with you in the home for more than half the year (except for temporary absences, such as school). However, if the qualifying person is your dependent parent, your dependent parent doesn't have to live with you.

See also this article from TurboTax for more information on qualified dependents.

You could get a larger standard deduction by filing as Head of Household, and could claim the Other Dependent Credit for your parents, but only if you qualify.

@Nero1