I'm not sure you should be editing the speed graph. Speed graphs are very hard to understand. You should be able to grab the square box and move the speed up or down.
Try editing the value graphs. If you want constant motion between keyframes you need to be changing the keyframe in the middle to a rove across time keyframe.
It would also help if you would show the reference graphs and tell us what property you're animating. I'm guessing that it's not position. In fact I have no idea what you're trying to do or even if you're trying to edit the speed graph because we can't see enough of your graph editor. Show us something like this:
Okay, I ended up rekeying it and it solved the issue.
The problem is that I'm used to working with bezier curves in the context of paths, so I failed to understand that the time constraints of the animation intrinsically change other areas of the curve, if that makes sense. Once that concept clicked with me, I found I was able to work with the graph display much better.
I'll keep your advice in mind about focusing on value graphs rather than speed graphs. In this particular case, I was solely interested in the speed of a camera zoom over time, so it ended up being the graph that I needed control over.
I sent you a PM earlier, dunno if you got it, but if not: thank you for your guidance. Between your responses to my questions, as well as your responses to others' questions that I found from searching, you've accelerated and deepened my understanding of AE.