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# Quadratics

### Algebra 2, Chapter 4

Term | Definition |
---|---|

parabola | the graph of a quadratic function |

axis of symmetry | a line through the graph of a parabola that divides the graph into two congruent halves |

vertex | the point at which the axis of symmetry intersects intersects the parabola |

quadratic function | a function that contains a quadratic term, a linear term, and a constant term |

maximum value | the greatest possible value a function can reach |

minimum value | the lowest possible value a function can reach |

quadratic equations | quadratic functions that are set equal to zero |

roots | solutions of a quadratic equation |

FOIL method | method that uses the Distributive Property to help multiply binomials |

pure imaginary numbers | square roots of negative real numbers |

complex number | any number that can be written in the form a+bi, where a and b are real imaginary numbers and i is the imaginary unit |

completing the square | a method that can be used to solve all quadratic equations by using the Square Root Property and manipulating the equation until one side is a perfect square |

discriminant | the expression b^2-4ac, which is used to determine the number and type of roots of a quadratic equation |

standard form | ax^2+bx+c=0, where a does not equal zero and a, b, and c are integers |

zeros | these are used to find the roots of a quadratic equation and are the x-intercepts of the graph of a quadratic equation |

factored form | 0=a(x-p)(x-q), where p and q represent the x-intercepts of a graph of the equation |

Zero Product Property | for any real numbers a and b, if ab=0, then either a=0, b=0, or both a and b equal zero |

imaginary unit i | i^2=-1; the number i is the principal square root of -1 |

Square Root Property | a method that is similar to a difference of squares and is used to solve quadratic equations |

factoring | finding the terms that are multiplied together to get an expression |