Here is another link for fertile egg pictures.
https://www.backyardchickens.com/threads/how-to-tell-a-fertile-vs-infertile-egg-pictures.16008/
I'll repeat what they said but maybe in a way that makes some of it easier to remember.
It takes about 25 hours, give or take an hour or two, for an egg to make its journey through the hen's internal egg making factory. That egg can only be fertilized in the first few minutes of that journey. That means if a successful mating takes place on a Monday, Monday's egg will not be fertile. Tuesday's egg might be but don't count on it. Wednesday's egg should be.
Not every mating is successful. The rooster may miss his target or he can elect to not eject sperm. The hen also has some control over whether or not she accepts that sperm or rejects it. There are reasons for that and most matings do result in fertility, but don’t assume because you see the act. Check for the bull’s eye.
At the end of the mating ritual the rooster hops off, his part is done. The hen then stands up, fluffs up her feathers, and shakes. This fluffy shake moves the sperm to a special container near where that egg starts its journey. As others said, the sperm normally remains quite viable for two weeks but after that viability can drop off. Don’t count on it past two weeks, but don’t be surprised if it lasts more than three.
As others said, a hen going broody is totally random. It has nothing to do with fertile eggs or if a rooster is present. Some hens will never go broody, some go broody a lot. Most of mine go broody mid-Spring to late-Summer but I have two that are still alternating going broody.