For part (a), just try using a couple values for C and you should be able to identify the general behavior of the graph. What happens when x=C? (Remember that we only care about the part of the graph from 0 to C, so ignore the rest of the graph.)
Here are a couple example graphs:
f(x)=sqrt(x)*(x-10)^2 - Wolfram|Alpha
f(x)=sqrt(x)*(x-5)^2 - Wolfram|Alpha
For part (b), your answer is correct.