I placed a bounty on this question to reward an existing answer. But it neither bumped to the homepage, nor can be seen on the bountied list. Where did my bounty go? When will it appear on the homepage?
This isn't by any means intended as a complete and definitive answer. (At least for some things I mention, I do not have a link to some kind of documentation saying this - they are mostly observations.) Still, I think that some of these things are useful to mention - and it is better to summarize them in an answer rather then leave them in multiple comments.
First, I will explicitly mention that a bounty bumps the question - so it will cause it to appear in various lists sorted by recent activity. (See the tag-info for bumping or the FAQ post: What can cause a question to be bumped?)
List of questions
If you look at the list of the questions, i.e., https://math.stackexchange.com/questions, you have several ways of sorting them. If you choose the active tab, you can see also the question where a bounty was started recently. The questions with bounties are shown also on the bountied tab. However, the sorting here seems to prioritize the bounties which are about to expire. Since at the moment there are 73 active bounties on this site, the recent ones will be at the bottom of the list. This means that to see your question, you have to go to the next page, even if your setting is to show 50 questions per page. (But over time it will get higher.)
One can also check the questions at https://math.stackexchange.com/ - I believe that this is commonly called the frontpage or the homepage.
- You have the tab of bounties, but it only shows 48 items. So your bounty will appear there later - I would guess that when this question will be among the top 48 in the list of bountied questions, it will appear also here.
- Mathematics does not have active tab on the frontpage - it has interesting tab instead. (If the information in the corresponding tag-info is up to date, Mathematics is one of the three sites that have the interesting tab. For example, if you go to https://mathoverflow.net/ you can see that you can choose the active tab. (Sorting in the interesting tab seems to be different - and rather complex. Still the description linked below says that it takes question's last activity into account. So a question that was bumped by a bounty should have bigger chance to appear there.)
- If you check active tab on some page that has this tab of even if you manually change the URL on Mathematics, you can see that a question appears in that list after it was bumped by a new bounty.
More details on selecting interesting questions.
This blog post describes in detail how the questions on the interesting tab are selected. (I do not know whether it was changed in some way since this was posted.)
In this process, several things are taken into account. Some of them are individual - top scoring tags and watched tags for a specific user. However, things such as score, number of answers, score of answers are the same for all users. You can see that this algorithm is more likely to choose questions which do not have highly upvoted answers. To be more specific, when counting the score, these are some factors:
|question score||+200 × score, up to +1,000 total|
|total answer score||-200 × score, up to -1,000 total|
|number of answers||-200 × answers, up to -1,000 total|
So in the specific case of the question you linked, you have +1000 since the question has score $\ge5$, then -1000 since the total score of the answers is $\ge5$, and then -600 since there are 3 answers. So if compared with a question where all other factors (tags, viewcount, last activity) are the same, this particular question automatically has difference of -600 in score.
Score can be increased if the question has some of your watched tags. Temporarily, I have added conic-sections and graphing-functions to my added tags. (These are both tags which the question currently has - and they are not very frequent, so I did not increase score for too many different questions.) After this the question is shown to me in the interesting tab somewhere around the middle of the page. Possibly another contributing factor was that I was looking relatively soon after you have edited the tags - which means more recent activity on the question. (When I display that tab in an incognito windows - as an anonymous user, so that the watched tags are no longer a factor - I do not see this specific question.)
- Bounty - Page 1 & 2 Differences - the answer mentions 48 questions shown on the home page.
- Stack Overflow interesting questions implementation and What is the list of interesting questions on stack overflow? - details about sorting in the interesting tab. The answers link to this blog post: Stack Overflow Homepage Changes.