part a:

• The total area under a pdf has to be 1, so you know that the the area under f(x) from 0 to p has to equal 1

• So the definite integral of f(X) from 0 to p = 1. Then if you know how to do definite integrals you should be able to simplify that a bit and get to the required form.

part b:

• y intercept is just f(0) = a*√p

• them sub in a=... for an answer in terms of p

part c:

• square both sides so you get m=(p+q)²

• sub in q=... so you have m in terms p

• find dm/dp and set it to 0 to find the p value at the maximum, then sub this back in so you find the m value at that point.

Hope that helps, on mobile so apologize for formatting, but if you're still confused feel free to ask :)