If I researched the car a lot and settled on a reasonable value would I be able to simply throw the number at them and not budge?

You can try, but be prepared to walk. They will almost NEVER accept the first offer you make unless you are offering their asking price. There is a game they play with this. The actual salesman you deal with usually doesn't have the authority to approve the sale, or at least he will pretend he doesn't. No matter what amount you offer, even if it's one dollar less than the asking price, the salesman will pretend to look insulted and crestfallen; he'll shake his head like he can't believe you would make such a low offer, and then he'll say, "Well...all I can do is go to the sales manager with your offer...but I don't think he will go for it". Then he'll go to the sale manager's office and they'll sit there and pretend to talk about it for a few minutes, and he'll come back and say, sorry, but we just can't go that low, you'll have to do better.

A few things I have learned:

Never get emotionally attached to a car you are dealing on, and above all don't reveal any emotional attachment or overt enthusiasm the salesman. Even if you think it is the perfect model, the perfect color, with perfect options and you're creaming your jeans over it...act like it is just one of many mundane choices you are considering. If they get a sense that you are hot and bothered about one particular car, they won't come down much in price.

Always have an alternative (or pretend to have one) and not-so-subtly let them know it. Have a list of other similar vehicles in your hand and let them see you consulting it. You might say things like, "You're price seems kinda high. There's a similar vehicle over at Joe's Car Sales for only $xxxx. That lets them know they have competition and that you might walk at any moment.

Go to a dealer near the end of a month when the sales people are eager to get one more sale on the books before the month-end cut off for their commission cheque.