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# Quadratic Functions

### Using forms of quadratic functions: standard, vertex, focus

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

Three points --> Standard Form | Substitute points -- Solve system with matrix |

Vertex & Point --> Vertex Form | Substitute point and vertex -- Find "a" |

Focus & Vertex --> Focus form | Substitute "c" -- Substitute vertex |

Standard Form --> Vertex Form | Use -b/2a to get vertex -- Use "a" value |

Vertex Form --> Standard Form | Expand the binomial square -- Simplify |

Vertex Form --> Focus Form | a = 1/4c |

Focus Form --> Vertex Form | a = 1/4c |

Standard Form --> Graph | Use -b/2a to get vertex -- "c" is y-intercept -- "a" is stretch factor |

Vertex Form --> Graph | (h, k) vertex -- "a" is stretch factor |

Focus Form --> Graph | (h, k) vertex -- "c" is focal length |

Standard Form Formula | y=ax^2 + bx + c |

Vertex Form Formula - Vertical Parabola | y=a(x - h)^2 + k |

Vertex Form Formula - Horizontal Parabola | x=a(y - k)^2 + h -- be careful of (h, k) placement |

Focus Form Formula - Vertical Parabola | y=1/4c(x - h)^2 + k |

Focus Form Formula - Horizontal Parabola | x=1/4c(y - k)^2 + h -- be careful of (h, k) placement |

Created by:
lajerauld