A quadratic equation is a second-order polynomial equation in a single variable

The general form is

where x represents a variable, and a, b, and c, represent coefficients and constants,

with a ≠ 0. (If a = 0, the equation becomes a linear equation.)

Among his many other talents, Major General Stanley in Gilbert and Sullivan's

operetta the Pirates of Penzance impresses the pirates with his knowledge of quadratic

equations in "The Major General's Song" as follows: "I am the very model of a modern

Major-General, I've information vegetable, animal, and mineral, I know the kings of

England, and I quote the fights historical, From Marathon to Waterloo, in order

categorical; I'm very well acquainted too with matters mathematical, I understand

equations, both the simple and quadratic, About binomial theorem I'm teeming with a lot

o' news-- With many cheerful facts about the square of the hypotenuse."

The constants a, b, and c, are called respectively, the quadratic coefficient, the

linear coefficient and the constant term or free term. Quadratic comes from quadratus,

which is the Latin word for "square." Quadratic equations can be solved by factoring,

completing the square, graphing, Newton's method, and using the quadratic formula.

One common use of quadratic equations is computing trajectories in projectile motion.

This module centers on the different ways of solving the quadratic equation by

factoring, by finding square roots, by completing the square, and by using the quadratic

formula. Students are given guides to determine the most appropriate method to use.

Identifying the disciminant of the quadratic equation and finding the relationship

between the coefficient and the root of the quadratic equation are also discussed.