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# c h a p t e r s i x

### Quadratic Functions

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

general quadratic expression | ax^2 + bx + c |

quadratic equation | ax^2 + bx + c = 0 |

quadratic function (standard form of a quadratic) | f: x --> ax^2 + bx + c |

Binomial Square Theorem | For all real numbers x and y, (x+y)^2 = x^2 + 2xy + y^2 and (x-y) = x^2 - 2xy + y^2 |

|-28| = ? | 28 (absolute value) |

what is the graph of the absolute value function? | f(x) = |x| an angle |

Graph-Translation Theorem | In a relation described by a sentence in xa dn y, the following two processes yield the same graph: (1) replacing x by x - h and y by y - k; (2) applying the translation T*h,k to the graph of the original relation. |

graph of the equation y = ax^2 + bx = c is a parabola congruent to the graph of what equation? | y = ax^2 |

Imaginary numbers | Square root of a negative number like -100 is 10i. Turn positive and add on imaginary number symbol (i) |

i^2 = ? | -1 |

Complex number | when a real number and an imaginary number are added. In the form of a + bi |

Discriminant Theorem | Suppose a, b, c are real numbers with a not equaling 0. Then the equation ax^2 + bx + c = 0 has (i) two real solutions if b^2 - 4ac > 0. (ii) one real solution if b^2 - 4ac = 0. (iii) two complex conjugate solutions if b^2 - 4ac < 0. |

Created by:
katelesperance