Calculus question

Hey guys, sorry to hit you with a homework thread, but I'm trying to help out my sister in college.  She's asking for help with this question and I've never taken a calculus class so I'm not totally clear on how to get the answer:

A sports field is to have the shape of a rectangle with semi-circles put on the two ends. It must have a perimeter of 1000 meters. What is the maximum area possible for the rectangular part.

I pretty much found the answer here http://www.ltcconline.net/greenl/courses/103a/keys/PracticeFinal/practiceFinaKeyl.htm on problem 11, but I don't know what "this can also be done by hand using the vertex of a parabola formula" means.  The rest of it makes sense to me.

Thanks for any help.

OK, the given information is that rectangle area A = x2r and x = 600 - pr where p is pi.  Rearrange the second equation to get r = (600-x)/p, then subsitute (600-x)/p for r in the area equation, to get A = 2x(600-x)/p = (1200x - x²)/p.  So Ap = -x[sup]2 + 1200x.  You should recognize that you've got an equation describing a parabola oriented so that its vertex is at the maximum.  You might have a formula available that finds the vertex based on A, B, and C values for an equation of the form Ax² + Bx + C = 0.