How do i come up with a good ap research topic?

I am not in AP research or anything, but I have done science fair and have competed at an international level, so I am somewhat qualified to answer this. If I were you I would look for problems that need to be solved, something that has a real world application. The other important criteria are that you enjoy what you are researching, there is nothing worse than constantly working on something you hate, and the feasibility. Are the resources there for you to do your project? If the idea meets these criteria you should have a pretty solid project. Hope this helps.

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You're asking in the ap section, so i'll give the ap calculus-style answer. alternatively, you can find the vertex of the parabola and use the "y"-coordinate as the answer.

the maximum height can occur at a critical number, that is, a number  such that  .

the derivative of  can be calculated as follows:



find a value of  that is a zero of the derivative:


this is parabola that is opening downward; we can assume there is a maximum at  .

to find that maximum, calculate  .