Your quote is built from inputs, and most of them are facts about the car, the way you drive it, and where you live. Before you argue about the total, find out which of those facts the pricing used, because some are fixed and some are recorded wrong more often than you might expect.
What the pricing reads
Providers and sellers price risk. The model class of the vehicle, its age, the miles on the odometer at sale, and its recorded condition all feed the calculation. Ask the seller to list the inputs in writing, not just the bottom line. A quote that names its inputs is much easier to check than one that only gives a total.
Use and location
How the car gets used and where it is kept can change the price. A vehicle driven for work, towing, or delivery runs may be priced differently from one used for commuting and errands. Where you live matters too, because repair labor rates and claim costs vary by region. If the quote assumes a use or location that does not match your life, correct it before you sign. A wrong answer on use can cause trouble later, including a disputed claim or a contract that is questioned after the fact.
The car's history
Ownership history and title history can narrow which contracts will accept the vehicle at all. A title that records prior damage, a rebuild, or a loss can change eligibility. Ask the seller whether the car's history was checked against the provider's rules, and ask how the quote would differ if that history were different.
What you can still change
Some inputs are fixed, such as the model year and the make. Others are facts you can correct, or choices you make at the desk. Ask which inputs can be changed after you sign and whether the price is recalculated if a wrong input is fixed. Keep the input sheet with your copy of the contract. The published tables on this site list the printed figures for each company, but the inputs behind any quote belong on paper before you decide.