## Definition

It's called a quadratic function, or polynomial function of the 2nd degree, any function *f* IR to IR given by a law of the form ** f (x) = ax ^{2} + bx + c**where a, b and c are real numbers and a 0. Let's look at some examples of quadratic functions:

- f (x) = 3x
^{2}- 4x + 1, where a = 3, b = - 4 and c = 1 - f (x) = x
^{2}-1, where a = 1, b = 0 and c = -1 - f (x) = 2x
^{2}+ 3x + 5 where a = 2, b = 3 and c = 5 - f (x) = - x
^{2}+ 8x, where a = -1, b = 8 and c = 0 - f (x) = -4x
^{2}where a = - 4, b = 0 and c = 0

## Graphic

The graph of a 2nd degree polynomial function, y = ax^{2} + bx + c, with a 0 is a curve called **parable**.

For example, let's build the graph of the function y = x^{2} + x:

We first assign x some values, then calculate the corresponding value of y, and then connect the points thus obtained.

x | y |

-3 | 6 |

-2 | 2 |

-1 | 0 |

0 | 0 |

1 | 2 |

2 | 6 |

Note:

When graphing a quadratic function y = ax^{2} + bx + c, we will always notice that:

if

**a> 0**, the parable has the**upward facing**;if

**a <0**, the parable has the**downward facing**;