If i started a business officially on 12/28/16, can i claim startup expenses previous to that

Yes you will be able to claim eligible start up costs on the day you first started your new business (see below).

You can start with the free version of TurboTax Online and if you need to upgrade to TurboTax Self-Employed (which may be required to report these business start-up cost), TurboTax will prompt you to upgrade (all information will be transferred automatically to the new upgraded version).

For the amount of start-up costs before you started your business -

You may elect to deduct up to $5,000 of start-up costs in the year your business begins operations. The $5,000 first-year deduction limit is reduced by the amount of start-up costs exceeding $50,000. (You would include this as under business income and expenses - "Other Common Business Expenses"> "Other Miscellaneous Expenses" and enter here (as start-up costs). 

Start-up costs that exceed the first-year limit of $5,000 may be amortized ratably over 15 years. The amortization period starts with the month you begin operating your active trade or business. (Include any remaining start-up cost under the asset section of business income and expenses.)

Start-up costs include amounts paid for the following:

• An analysis or survey of potential markets, products, labor supply, transportation facilities, etc.
• Advertisements for the opening of the business.
• Salaries and wages for employees who are being trained and their instructors.
• Travel and other necessary costs for securing prospective distributors, suppliers, or customers.
• Salaries and fees for executives and consultants, or for similar professional services.

For example, you began business operations July 1, 2016, had start-up costs of $35,000.

You may deduct $6,000 in 2016 (First-year limit, $5,000, plus First year's amortization, $1,000).

A full year's amortization would be $2,000 ($35,000 minus $5,000 divided by 15). Since  the amortization period began July 1, 2015 (the month business operations began), the first year's amortization is one half of $2,000 or $1,000.

For the amount of business expenses after you started your business -

You will be able to expense any eligible business costs incurred after you started your business.

Please refer to this IRS link for more information about Business Expenses