So I have a horizontal banner that I defined via a div. This div has a width of the full window and fix height of 500px for the time being. How can I scale an background image (2048 x 1283) to fill the div entirely without loss of picture quality? How would I do the same if the div height was relative to the window size, perhaps 25% or 50%? I want this to work when the window is resized.
Well you will never loss picture quality because you are keeping rendering the same picture over different sizes. You have to understand that responsive background its a hard topic since the picture will never display exactly how you want to, since different devices will have different display resolution, as example if you are seeing the same responsive image in your iphone portrait format (vertically) will look smaller in height than if you see in the same device but in landscape format (horizontal).
Any way heres is a question that can help you in your journey of responsive backgrounds Responsive css background images
cheers.
--- EDIT
if you want to achieve a full background http://css-tricks.com/perfect-full-page-background-image/ see this information.