Consider the quadratic function y=x^2+2x-3.

Now we shall calculate some y-values by substituting x-values from -5 to +5.

x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |

x^2 | 25 | 16 | 9 | 4 | 1 | 0 | 1 | 4 | 9 | 16 | 25 |

2x | -10 | -8 | -6 | -4 | -2 | 0 | 2 | 4 | 6 | 8 | 10 |

-3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 | -3 |

y | 12 | 5 | 0 | -3 | -4 | -3 | 0 | 5 | 12 | 21 | 32 |

y | 12 | 5 | 0 | -3 | -4 | -3 | 0 | 5 | 12 | 21 | 32 |

1st difference | 7 | 5 | 3 | 1 | -1 | -3 | -5 | -7 | -9 | -11 | |

2nd difference | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

The first differences between the terms are all different.(Got by subtracting the consecutive y-values)

However, if you look at the differences between these first differences they go up in steps of 2.

We can state that the second difference is 2.

This means that it is a quadratic sequence.

**A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant**.