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Warm Up

Warm Up. What is the standard form of a parabola? What is the standard form of a circle? What is the standard form of a ellipse? What is the standard form of a hyperbola?. Algebra 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 6: Graphing and Classifying Conics. VOCAB.

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Warm Up

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  1. Warm Up • What is the standard form of a parabola? • What is the standard form of a circle? • What is the standard form of a ellipse? • What is the standard form of a hyperbola?

  2. Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

  3. VOCAB • Conics or Conic Sections – parabolas, circles, ellipses, and hyperbolas…basically all curves that are formed by the intersections of a plane and a double-napped cone • Discriminant – an equation that can tell what type of conic you have

  4. Classifying – way 1 • Today we are going to learn one way to classify a conic section. This way is to put it in a normal formula.

  5. Formulas • Parabola • or • Circle • Ellipse • or • Hyperbola • or

  6. Directions • Look at the powers of x and y • If ONLY one of them is squared…parabola • Get x and y on the same side • Divide by the number • If it is SUBTRACTION…Hyperbola • If it is ADDITION • Denominators are the same…Circle • Denominators are different…Ellipse

  7. I DO (Classifying) • Classify the conic section • 1. • 2. • 3. • 4.

  8. WE DO (Classifying) • Classify the conic section • 1. • 2. • 3. • 4.

  9. YOU DO (Classifying) • Classify the conic section • 1. • 2. • 3. • 4.

  10. Review • What did you learn today?

  11. Homework • NONE

  12. Warm Up • Name the 4 types of conic sections • Explain how to classify a conic section

  13. Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

  14. Classifying – discriminant • Today we are going to learn one way to classify a conic section. This way is to find the discriminant

  15. Formulas • General Equation • Discriminant

  16. KNOWLEDGE • Discriminant • Less than zero • B = 0 and A = C …it’s a circle • B ≠ 0 or A ≠ C … it’s an ellipse • Equal zero • It’s a parabola • Greater than zero • It’s a hyperbola

  17. DIRECTIONS • Find a, b, c • Find the discriminant • Classify the conic

  18. I DO (Classifying) • Classify the conic section • 1. • 2. • 3. • 4.

  19. WE DO (Classifying) • Classify the conic section • 1. • 2. • 3. • 4.

  20. YOU DO (Classifying) • Classify the conic section • 1. • 2. • 3. • 4.

  21. Review • What did you learn today?

  22. HOMEWORK • Worksheet • 10.6B (9 – 14)

  23. Warm Up • Classify the conic • 1. • 2.

  24. Algebra 3Chapter 10: Quadratic Relations and Conic SectionsLesson 6: Graphing and Classifying Conics

  25. TODAY • Today we are going to learn how to write equations of conics that are NOT in the center of a graph

  26. Formulas • Parabola • or • Circle • Ellipse • or • Hyperbola • or

  27. CENTER • Center of all shapes is • (h , k) • A is the distance from the vertex to the center • C is the distance from the focus to the center

  28. Directions • Label what you know • Find what your missing • A, b, c, p, h, k • Plug into the

  29. I DO (Equations) • Write the equation of the conic section • 1. Parabola … V (-2, 1) F (-3, 1) • 2. Circle … Center (3, -2) r = 4 • 3. Ellipse … F (3, 5) (3, -1) V (3, 6) (3, -2) • 4. Hyperbola … V (5, -4) (5, 4) F (5, -6) (5, 6)

  30. WE DO (Equations) • Write the equation of the conic section • 1. Parabola … V (1, -2) F (1, 1) • 2. Circle … Center (9, 3) r = 4 • 3. Ellipse … V(2, -3) (2, 6) F (2, 0) (2, 3) • 4. Hyperbola … V (-4, 2) (1, 2) F (-7, 2) (4, 2)

  31. YOU DO (Equations) • Write the equation of the conic section • 1. Parabola … V (-3, 1) directrix x = -8 • 2. Circle … Center (-4, 2) r = 3 • 3. Ellipse … F (-2, 2) (4, 2) CV (1, 1 (1, 3) • 4. Hyperbola … V (8, -4) (8, 4) F (8, -6) (8, 6)

  32. Review • Today you learned how to write the equation of a translated conic

  33. HOMEWORK • Worksheet • 10.6B (1 – 4)

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