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Understanding Conic Sections: Domain, Range, and Graphing Strategies

This lesson covers the fundamentals of conic sections formed by the intersection of a plane and a double cone. We explore concepts such as domain and range in equations and how to graph conic sections like circles, ellipses, and hyperbolas. Students will learn to identify key features of conics, including their center and intercepts, and work collaboratively to reinforce their understanding through partner practice. Engage effectively with graphs using calculators and manipulatives, fostering a deeper grasp of mathematical concepts.

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Understanding Conic Sections: Domain, Range, and Graphing Strategies

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  1. ACT Opener: • Find when x= -6 and y = 3. a) -9 b) 54 c) 81 d) 126 e) 198

  2. Conic Sections!

  3. Conics Sections • A conic section is a curve formed by the intersection of a plane and a double cone. By changing the inclination of the plane, you can create a circle, a parabola, an ellipse, or a hyperbola.

  4. Quick Review: Domain & Range • What is domain and what is range? • How are the related to x and y in an equation?

  5. Quick Review: Domain & Range • Find the domain and range of the following equation:

  6. Example 1: Graphing a Circle • Graph the equation Describe the graph and its lines of symmetry. Then find the domain and range.

  7. Example 1: Graphing a Circle • How could we graph this using our calculators? • How would we have to manipulate the equation? • Why is there no point on the graph with an x-coordinate of 6?

  8. Student Check: • Graph the Equation . Describe the graph and the lines of symmetry. Find the domain and range. • Use your white boards.

  9. Student Check: • What is the shape of your graph? • How would we manipulate the equation so that we could graph it in the calculator?

  10. Interpreting Graphs • Identify the center and intercepts of the conic section. Then identify the domain and range.

  11. Student Check: • Identify the center and intercepts of the conic section. Then identify the domain and range.

  12. Partner Practice: • Pair up with your partner to complete the problem set. • Only complete the problems that have been circled. • You will have 15 minutes to complete.

  13. Partner Practice: Group 1: Justin & Tristan Group 2: Harley & Andrea Group 3: Kelly & Jessica Group 4: Taylor & Brando Group 5: Samantha & Trevor

  14. Exit Slip: Identify the domain and range of the following conic section. Domain: Range: Domain: Range: • The graph of which equation of a circle contains only the points in the table.

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