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The Conic Sections

Quadratic Functions. The Conic Sections. What Are Conic Sections?. The First: The Parabola. THE SECOND: THE CIRCLE. The Third: The Ellipse. The Fourth: The Hyperbola. 8x 2 +7y 2 = 4 4x – 3 = y 2 5y - 8x 2 = 1 9x 2 - 4y 2 = 3 2y 2 = 7x 1.7y = 2.3x 2 2x 2 + 5x - 3y + 15y 2 = 1.

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The Conic Sections

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  1. Quadratic Functions The Conic Sections

  2. What Are Conic Sections?

  3. The First: The Parabola

  4. THE SECOND: THE CIRCLE

  5. The Third: The Ellipse

  6. The Fourth: The Hyperbola

  7. 8x2 +7y2 = 4 4x – 3 = y2 5y - 8x2 = 1 9x2 - 4y2 = 3 2y2 = 7x 1.7y = 2.3x2 2x2 + 5x - 3y + 15y2 = 1 And Then The Algebra…

  8. y2 + 2y + x2 + 6x = 6 (y2 + 2y + 1) + (x2 + 6x + 9) = 6 + 1 + 9 (y + 1)2 + (x + 3)2 = 16 You’ll Still Need Complete the Square…But Now You’ll Use it Twice!

  9. A parabola is a set of points that are equidistant from a point (focus) and a line (directrix) that does not go through that point. And The Pieces Get More Complicated…

  10. An ellipse is a set of points where the sum of the distances from the foci to each point stays constant In this case, each point will have d1 + d2 equal the same thing. And More Complicated…

  11. Each point on a hyperbola has the same difference of distances from the two foci. And Even More Complicated…

  12. WHAT!!!

  13. And Then You Need to Graph!

  14. And On Top of All That, 2 Weeks…

  15. Parabolas • Axis of Symmetry • Focus • Directrix • Graphing • Non-function parabolas BUT IT ISN’t ALL THAT MUCH INFORMATION

  16. Ellipses and Circles • Major Axis • Minor Axis • Center • Foci • “The Box” • Graphing WELL, Maybe it’s a bit more information Than I originally Thought.

  17. Hyperbolas • Foci • Center • Asymptotes • Major Axis • Directrices • Graphing Just a little bit more

  18. How much money will the company make during its first three months after incorporation? Graphing Calculators The Good News

  19. So CHEER UP AND LET’s GET STARTED!

  20. But you don’t really need to worry about that because we’ll talk about all of this information in the next two weeks. Sincerely, AG VISit Me On The Website

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