# 008A Sample Final A, Question 6

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**Question: ** Sketch . Give coordinates of each of the 4 vertices of the graph.

Foundations |
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1) What type of function is this? What type of graph is this? |

2) What can you say about the orientation of the graph? |

Answer: |

1) Since both x and y are squared it must be a hyperbola or an ellipse. Since the coefficients of the and terms are both positive the graph must be an ellipse. |

2) Since the coefficient of the term is smaller, when we divide both sides by 36 the X-axis will be the major axis. |

Solution:

Step 1: |
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We start by dividing both sides by 36. This yields . |

Step 2: |
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Now that we have the equation that looks like an ellipse, we can read off the center of the ellipse, (0, -1). |

From the center mark the two points that are 3 units left, and three units right of the center. |

Then mark the two points that are 2 units up, and two units down from the center. |

Step 3: |
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Now draw an oval through the four points you just drew. |

Final Answer: |
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Now draw an oval through the four points you just drew. |