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# CME Algebra 2

### Chapter 1

Question | Answer |
---|---|

balance point | the point(x,y) with the x-coordinate that is the AVERAGE of all the x-coordinates in the table and with the y-coordinate that is the AVERAGE of all the y-coordinates in the table (p.44) Also known as a "centroid" in geometry. |

closed-form definition | a function that lets you find any output [f(n)] for any input [n] by DIRECT calculation |

cubic function | a function defined by a polynominal in which the highest-degree term is cubed, and generally looks like "ax^3+bx+c |

difference table | a table that helps you see patterns that lead to recursive definitions p.10 |

hockey stick property | To find the next OUTPUT in a table, add (the sum of ALL the DIFFERENCES so far and the single FIRST OUTPUT of the table). |

line of best fit | given a set of data, the line that minimizes the sum of the squares of the errors (or it minimizes the mean squared error), and contains the balance point. |

mean absolute error | the average of the absolute values of the errors (or lengths of the outlier points from the line) |

outlier | a data point (x,y) that lies outside, or far away, from the rest of the data |

quadratic function | a function defined by a polynominal in which the highest-degree term is squared, and generally looks like "f(x)=ax^2+bx+c." |

recursive definition | a function that expresses patterns in the outputs of a function p.9 |

Theorem 1.2 | If "f(x)=ax+b" is a linear function, its differences are constant. |

Theorem 1.1 | An input-output table with a constant differences can be matched with a linear function. The slope of the graph is the constant difference in the table. |

Rise/Run | change in output/change in input |

Difference | the amount to add to move from one output to the next output |

Up-and-over property | Add (the previous output and the difference) onto the next output when writing a recursive function |

Theorem 1.3 | For any quadratic function, the second differences are constant. The constant second difference is 2a, (or twice the coefficient of the squared term). |

factoral function, n! | a function that has a "n!" where "n!" is the product of all the intergers from 1 to n. This function has no simple closed form. |

Created by:
Fortier Family