In most states the amount subject to sales tax is the price of the new car minus your trade-in allowance. Be sure that you have a completed, signed contract before you drive your new car from the dealership. It's much easier to spot errors and make corrections now. If you should have trouble, the Federal Trade Commission may be able to help. You might also want to check with your States' Attorney.
Many states have laws to protect new car buyers.
Your car is the second most expensive item you own. This is one purchase where extra time and effort pays big dividends. There's even a free weekly email newsletter. All rights reserved unless specifically noted. All advice should be weighed against your own abilities and circumstances and applied accordingly.