What does quadratic mean?
The word quadratic comes directly from the Latin word quadratus, which means a square. As the English language evolved, we began to use the prefix quad to mean four, which is why a foursided shape is called a quadrilateral and a fourwheeled bike is called a quad bike.
However, when we use the word "quadratic", we are referring back to the original meaning of the word. If something (an expression or equation) is quadratic, it is to do with squares. A quadratic expression is anything with x² as its highest power. So the following expressions would all be quadratics:
In addition, squares are associated with areas. Square numbers can be used to make shapes, and we use square units when calculating areas. The formula for the area of a circle is quadratic (it uses r²). Originally, quadratics were used as a way to represent problems involving unknown areas. 
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