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

# Quadratic Functions

### Quadratic Functions and Graphs

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

When k in the equation y=a(x-h)^2+k is negative, what happen? | The parabola shifts DOWN (A part of your vertex). Example: y=x^2-7, the parabola will shift DOWN 7 units (vertex: (0,-7)) |

When k in the equation y=a(x-h)^2+k is positive, what happen? | The parabola shift UP (A part of your vertex). Example: y=x^2+2, the parabola will shift UP 2 units (vertex: (0,2)) |

When h in the equation y=a(x-h)^2+k is negative, what happens? | The parabola shifts RIGHT (A part of your vertex). Example: y=(x-3)^2, the parabola will shift RIGHT 3 units (vertex: (3,0)). Another way to remember: If it's in parenthesis, it will do the opposite. |

When h in the equation y=a(x-h)^2+k is positive, what happens? | The parabola shifts LEFT (A part of your vertex). Example: y=(x+4)^2, the parabola will shift LEFT 4 units (vertex: (-4,0)). Another way to remember: If it's in parenthesis, it will do the opposite. |

What does the a in the equation y=a(x-h)^2+k do? | This dictates whether the parabola will WIDEN or become more NARROW. Example: y=1/4x^2 will WIDEN y=5x^2 will become more NARROW |

What will the equation: y=(x-3)^2+7 look like on a graph? | A parabola shifted RIGHT 3 units and UP 7 units. Vertex: (3,7) |

What will the equation: y=(x+2)^2-3 look like on a graph? | A parabola shifted LEFT 2 units and DOWN 3 units. Vertex: (-2,-3) |

What will the equation: y=1/3(x-4)^2+6 look like on a graph? | A parabola shifted RIGHT 4 units, UP 6 units, and wider. Vertex: (4,6) |

If given a quadratic equation in standard form (ax^2+bx+c), how can you find the vertex? | The 'Vertex Formula': -b/2a will give you the x part of your vertex. Then plug in the x and solve for y. |

What is the vertex for y=x^2+6x-7? | -6/2(1)= -3 (-3)^2+6(-3)-7= -16 Therefore, your vertex is: (-3,-16) |

How do you find the y-intercept? | Replace x with 0 and solve for y. Example: y=(x-2)^2-1, y-intercept: (0,-1) y=x^2+4x-6, y-intercept: (0,-6) NOTE: THERE WILL ALWAYS BE A Y-INTERCEPT BUT NOT ALWAYS A X-INTERCEPT. |

How do you know if a parabola faces upwards or downwards? | Look at your y=a(x-h)^2+k, if a is a POSITIVE then it faces UPWARDS, if a is a NEGATIVE, then it faces DOWNWARDS. |

Created by:
careyann