Math Puzzler #1

I'm going to post math problems, both those I write, and those I find interesting. So for the first math problem!
Two quadratics both pass through opposite corners of a rectangle whose sides are parallel to the xy-Cartesian axes. One quadratic has it's vertex on the lower left corner, but also passes through the upper right corner, and the second has it's vertex on the upper right, but also passes through the lower left. These two quadratics form a region within the rectangle. What fraction of the area of the rectangle is the area of this region?


On grades

This week has not been my best. The long and short of it is that my academics is in, if not dire, at least mediocre straits, and I have no one to blame but myself, as usual. The damage I've done is not horrible, and with hard work over the next few weeks, I can mostly erase it, but it falls inconveniently across a progress report, so I will likely catch some flack from my parents. More than that though, I've realized that I've been, up to now, motivated out of fear of my parents.
My academic goals are not really my own, and that needs to change. It isn't the first time I've realized this, but nevertheless, I truly want to change this. A first step, I figure, is putting my thoughts into words on a page, so I can comeback and revisit my conviction when I feel unmotivated in the future.