### Introduction

A
**
quadratic equation
**
is one which can be written in the form
$a{x}^{2}+bx+c=0$
where
$a$
,
$b$
and
$c$
are numbers,
$a\ne 0$
, and
$x$
is the unknown whose value(s) we wish to find. In this Section we describe several ways in which quadratic equations can be solved.

#### Prerequisites

- be able to solve linear equations

#### Learning Outcomes

- recognise a quadratic equation
- solve a quadratic equation by factorisation
- solve a quadratic equation using the standard formula
- solve a quadratic equation by completing the square
- interpret the solution of a quadratic equation graphically

#### Contents

1 Quadratic equations2 Solution by factorisation

3 Completing the square

4 Solution by formula

5 Engineering Example 1

5.1 Undersea cable fault location

6 Engineering Example 2

6.1 Estimating the mass of a pipe

7 Geometrical representation of quadratics