A quadratic equation is a multi-termed equation (polynomial) which has the form ax²+bx+c=0. It is called quadratic because the leading term has a squared variable and quadratus is Latin for "square".
Backstory
The quadratic equation arose from a need that ancient mathematicians had — to calculate the lengths of the sides of a figure, when the area was known. In other words, if they knew the total amount of square feet they needed for a building of a certain shape, how long should each side be? The initial problem prompted centuries of mathematical work, resulting in the quadratic equation that students study in algebra today.BBC h2g2: The History Behind The Quadratic Formula