## The Lesson

A quadratic equation is an equation in the form:-
**x**is a variable. It is an unknown. -
**a**,**b**and**c**are constants, where**a**cannot equal 0. They stand in for numbers.

## Dictionary Definition

The Oxford English Dictionary defines a quadratic equation as "an equation of the second degree; specifically an equation of the form*ax*, where

^{2}+ bx + c = 0*a*,

*b*, and

*c*are constants and

*x*is unknown."

## Understanding Quadratic Equations

It is easier to understand quadratic examples with an example. Let's look at a quadratic equation. This is the quadratic equation shown at the start of the lesson with**a**= 2,

**b**= 3 and

**c**= 4. This a

**quadratic**equation because of the

**x**. A quadratic equation is an equation where the highest

^{2}**power**of

**x**is

**2**.

## What Quadratic Equations Are...

Here are some real examples of quadratic equations. They are all in the standard form**ax**:

^{2}+ bx + c = 03x^{2} + 5x + 2 = 0 |
a = 3, b = 5, c = 2 |

x^{2} + 4x + 3 = 0 |
a = 1, b = 4, c = 3 (no need to write 1x^{2}) |

x^{2} − 4x + 4 = 0 |
a = 1, b = −4, c = 4 |

x^{2} = 2 − 5x |
This looks different because some terms have been moved to the other side of the equals sign. |

4x^{2} + 1 = 0 |
There is no x term (so b = 0), but the highest power of x is still 2. |

2(x^{2} − x) = 3 |
The left hand side is factored and another term has been moved to the other side of the equals sign. |

x(x + 2) = 0 | When the bracket is expanded, you get a x term.^{2} |

## ...And What Quadratic Equations Aren't

These equations are**not**quadratic equations:

x + 2 = 0 | There is no x term (a = 0). This is a linear equation.^{2} |

x^{3} + 2x^{2} + 3x + 4 = 0 |
There is a x term. The highest ^{3}power of x is 3, not 2. This is a cubic equation. |

## The Graph of a Quadratic Equation

A quadratic equation can be plotted on a graph. Plot the function: The graph of a quadratic equation looks like a curve:-
**y**and**x**are the**Cartesian coordinates**of the points on the curve.

## What's in a Name?

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