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The curve isn't a curve, it's a metaphor.
There is no curve. There is a rough inverse relationship. The relationship will very likely have discontinuities in it. It will not be smooth. For small sales volume, it will suffer from statistical noise.
The only way to plot the graph (not curve) is empirically. The graph cannot be calculated accurately ahead of time.
Given very large sales volumes and steady conditions, it may be possible to estimate the graph usefully based on historical conditions and a rational assessments of the effects of price points. I'd expect this to be true for large corporations selling many units of a single item in a mature market without any external shocks. In those conditions, you may get a significant figure or two out of a numerical estimate given an existing empirical base of price change data.
For more open conditions - don't waste your time. The relationship is metaphorical at best, and just plain wrong at worst.
Really? Oh yes.
Here's a data point - at this year's Big Green Gathering a company was giving away free bottles of water.
Water is a very desirable resource at festivals, especially on hot days. If supply and demand were true you'd expect the stall to be mobbed. People would rather get something free than not, wouldn't they?
In reality - not so. The stand got some interest, and it did - eventually, after a week or so - run out of water. But it didn't get a lot more interest than other stands, and people were still paying for bottles of water elsewhere on the site.
You can explain this by looking at how and why people buy water. (There's more going on than simple thirst.)
You can't explain it by looking at a simple-minded supply and demand curve, because it really is much too crude and clumsy a tool to be useful as a model in most real situations.
Alternatively - will some stall holders charge more for water when it's hot? At some festivals, yes they will.
Can you calculate how much more? No, you can't. You can guess based on what you think is likely and reasonable - and the chances are their guess will be similar to yours, at least within 50p or so.
No one is going to sell water for £10,000 a bottle. They might try £3 if they think they can get away with it. £2 is more likely.
And so on.
But empirically, from first principles? No.
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