Follow Us on Twitter

What Is a Quadratic Equation? (Mathematics Lesson)

What Is a Quadratic Equation?

A quadratic equation is an equation in the form:

y equals a x squared plus b x plus c

On a graph, a quadratic equation looks like a curve:

quadratic equation on a graph

Understanding Quadratic Equations

Let's look at a quadratic equation:

y equals 2 x squared plus 3 x plus 4

It is the x2 that makes it a quadratic equation.

A quadratic equation is an equation where the highest power of x is 2.

We see x in two places:

  • x appears with a coefficient of 2 in front of it (2x).

  • x appears as x2. This is x with an exponent of 2.

It appears on its own (x) and with an exponent of 2 (x2) which is said as "x squared".

Real Examples of Quadratic Equations

Some examples of quadratic equations are shown below. The values of the constants a, b and c are written next to them:

examples of quadratic equations

Solving Quadratic Equations

Solving a quadratic equation means finding the value of x that make y = 0:



The values of x are the roots of the quadratic equation.

There are 3 main ways of solving quadratic equations:

Curriculum
Algebra Lessons
Interactive Widget
Here is an interactive widget to help you learn about quadratic equations.
Interactive Test
  show
 
Note
WHAT'S IN A NAME?

The word 'quadratic' comes from the word 'quad', meaning "square" - because the x is squared.

DIFFERENT FORMS OF QUADRATIC EQUATIONS

The many different forms of linear equations may be quite confusing. But they all have some things in common:

  • There are 2 variables, y and x.

  • There are constants, like 2 or c.

  • The highest power of x is 2.

    If the highest power of x is 1, (i.e.
    a = 0 in the standard form), it is a linear equation:



    These are quadratic equations, not linear equations.

    Neither will you see powers of 3 (cubic equations) or higher:

Y-INTERCEPT

The y-intercept is found by inserting x = 0 into the quadratic equation. This gives:



THERE ARE 2 ROOTS

Quadratic equations always have two solutions.



Sometimes it seems that there is only one root, but it is repeated.



Even when it seems there are no roots, there are two complex roots.