The Original Problem 2000(or so) BC Egyptian, Chinese and Babylonian engineers were actually smart people - they knew how the area of a quadrangle scales with the length of its side. They knew that it's attainable to store nine times more bales of hay if the side of the square loft is tripled. They moreover found out how to calculate the area of more complex designs like rectangles and T-shapes and so on.
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There are linear functions and there are quadratic functions but I am not aware of a linear quadratic function. It probably comes from the people who worked on the circular square.
There are different methods of using quadratic functions depending on the equation.
All quadratic functions with real coefficients can be graphed on a standard x-y graph. Not all quadratic functions have real roots, maybe that's what you were thinking of?
Blue Waffles
Yes