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# Module 9

### This will contain important information covered in Module 9

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

Product Property of Radicals | For a >= 0 and b >= 0, square root of ab = square root of a * square root of b |

Quotient Property of Radicals | For a >= 0, and b >= 0, square root of a/b = square root of a/square root of b |

Find the square root of "+" or "-" of 12. | +- 2 square root of 3 |

Square root of +- 0.27. | +- 3*square root of 3/10 |

From the equation 4x^2 - 5 = 2 what is the equation that represents this? Solve. | ax^2 - c = 0 x = +- 1.32 |

Solve 2x^2 - 8 = 0. | x = +- 2 |

When you look at a function on a graph what are the x-intercepts and what are the solutions? | x - intercepts = roots of the equation solutions = zeros of the equation |

Solve 3x^2 + 6 = 33. | x = +- 3 |

What equation is represents (x+5)^2 = 36. Solve. | a(x+b)^2 = c x = -11 and x = 1 |

Solve 2(x-3)^2 = -32. Is is a solution or no solution? | square root of (x-3)^2 = square root of -16 no real solution |

A contractor is building a fenced-in playground at a daycare. The playground will be rectangular with its width equal to half its length. The total are will be 5000 square feet. Determine how many feet of fencing the contractor will use | P = 100 ft |

What is completing the square? | a process of rewriting a quadratic expression as a perfect square trinomial so that it can be solved by taking square roots |

Complete the square for x^2 + 4x. | (x+2)^2 |

Complete the square, x^2 - 4x = 3 (x^2 + bx + c = 0). | x = 2+-square root of 7 |

Complete the square 4x - 8x = 21 (ax^2 + bx + c = 0 -- a is a perfect square) | x = 7/2 and x = -3/2 |

Complete the square 2x^2 - 6x = 5 (ax^2 + bx + c = 0 -- a is not a perfect square) | x = 3+-square root of 19/2 |

What is the quadratic formula? | x = -b+-square root of b-4ac/2a |

What is the standard form of a quadratic equation? | ax^2 + bx + c = 0 |

What is the discriminant? | b^2 - 4ac |

A diver jumps from a platform 10 meters above the surface of the water. The diver's height is given by the equation h = -4.9t + 3.5t + 10, where t is the time in seconds after the diver jumps. For what time t is the diver's height 1 meter? | 188.65 |

What methods can you use to solve quadratic equations? ' | factor (x-method), square root, graph, complete the square, quadratic formula |

Factor x^2 + 7x + 6 = 0, square root of (x+3)^2 = square root of 49, 25x^2 - 36 = 0. Use different methods | 1. x = -6 and x = -1 -- x-method 2. x = 4 and x= -10 -- square root 3. x +-6/5 -- complete the square |