Lesson Introduction into Quadratic Equations

I am writing this lesson so that it contains everything you need to solve quadratic equations and do well on tests. Other quadratic lessons in this module explain the fine points of quadratics if you are interested. You can also try the quadratic equation solver that also shows you a graph.

What is a quadratic equation

A quadratic equation is an equation of form that involves only two things besides numbers: a variable and a square of this variable. Examples: , , and so on. Usually, they are arranged so that the square part goes first, then the part with the variable, and some constant, equal to zero. In your tests, a, b and c will be actual numbers.

Solving Quadratic Equations

There are two ways of solving quadratics: factoring and using the Quadratic formula (see solver). Of these methods, the Quadratic Formula is the most reliable method that will give you the correct answer without guesswork. Here's how it works.

Let's say that you have an equation . If your equation is in some other form, for example , convert it to standard form with first, x part second, and the number third. The previous example , for example, converts to .

First, compute the discriminant. . You need to remember this formula. The discriminant can be positive, zero, or negative.

If the discriminant is positive, the equation has two different solutions (roots). One solution is . The other solution is . Click here to read the proof of these formulas. These solutions are so similar, that they are often written as . The +/- sign means that one solution comes with a "+" sign, and the other with a "-" sign.