Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# SarahDavis PrCalc1.7

### Sarah Davis Precalculus 1.1-1.7

Formula/Equation/Property Name | Definition |
---|---|

Distance Formula | d=SqRt[(x2 - x1)^2 + (y2 - y1)^2] |

Midpoint Formula | (x,y) = ( (x1+x2)/2, (y1 + y2)/2 ) |

Slope | m = (y2 - y1)/ (x2-x1) , if x1 NOT EQ x2; undefined if x1 = x2 |

Parallel Lines | Equal Slopes (m1 = m2) |

Perpendicular Lines | Product of slopes is -1 (m1 * m2 = -1) |

Vertical Line | x = a, where "a" is a constant number |

Horizontal Line | y = b, where "b" is a constant number |

Point-Slope form of the equation of a line | y - y1 = m(x - x1); "m" is the slope of the line, (x1, y1) are the coordinates of the point on the line |

GENERAL form of the equation of a LINE | Ax + By + C = 0, A, B not both 0 |

Point-Slope-Intercept form of the equation of a line | y = mx + b; "m" is the slope of the line, "b" is the y-intercept |

STANDARD form of the equation of a CIRCLE | (x - h)^2 + (y - k)^2 = r^2; "r" is the radius of the circle, (h,k) are the coordinates of the center of the circle |

GENERAL form of the equation of a CIRCLE | x^2 + y^2 + ax +by +c = 0 |

Equation of the Unit Circle | x^2 + y^2 = 1 |

Quadratic Equation | ax^2 + bx + c = 0, where "a" NOT = 0 |

Quadratic FORMULA | x = [-b plus or minus SqRt(b^2 - 4ac)] /(2a) AND (b^2 - 4ac) NOT negative; in the quadratic equation "a" is the coefficient of x^2, "b" the coefficient of x, and "c" is the pure numerical term. |

Discriminant | in the quadratic formula, b^2 - 4ac |

Quadratic Equation has 2 REAL DISTINCT solutions | the discriminant b^2 - 4ac > 0 |

Quadratic Equation has 1 REAL solution REPEATED | the discriminant b^2 - 4ac = 0 |

Quadratic Equation has NO REAL solutions | the discriminant b^2 - 4ac < 0 |

Trichotomy Inequality Property | a < b or a = b or b < a "2 numbers are related to each other by one of the above 3 ways" |

Transitive Property of Inequality | If a < b AND b < c, THEN a < c. If a > b AND b > c, THEN a > c. |

Addition Property of Inequality | If a < b, THEN a + c < b + c. "If a first quantity is less than a second quantity, the same amount can be added to both quantities, and the new first quantity will still be less thant the new second quantity." If a > b, then a + c > b + c. |

Multiplication Property of Inequality: 2 quantities (a < b) multiplied by the same positive number | If a < b and if c > 0, then ac < bc. "The resulting new first quantity is still less than the resulting new second quantity." |

Multiplication Property of Inequality : 2 quantities (a < b) mulitplied by the same NEGATIVE number | If a < b and if c < 0, then ac > bc "The resulting new first quantity is then GREATER than the resulting new second quantity." |

Multiplication Property of Inequality: 2 quantities (a > b) multiplied by the same positive number | If a > b and if c > 0, then ac > bc. "The resulting new first quantity is still greater than the resulting new second quantity." |

Multiplication Property of Inequality : 2 quantities (a > b) mulitplied by the same NEGATIVE number | If a > b and if c < 0, then ac < bc "The resulting new first quantity is then LESS than the resulting new second quantity." |

Reciprocal Property of Inequality: a > 0 | (1/a) > 0 |

Reciprocal Property of Inequality: a < 0 | (1/a) < 0 |

Absolute value: |u| = a, a > 0 | u = -a OR u = a |

Absolute value: |u| <or= a, a > 0 | -a <or= u; u <or= a. |

Absolute value: |u| >or= a, a > 0 | u <or= -a; u >or= a. |

Created by:
DDavis