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 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 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

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)

8. WE DO (Classifying)

9. YOU DO (Classifying)

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 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 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

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)

19. WE DO (Classifying)

20. YOU DO (Classifying)

21. Review What did you learn today?

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

23. Warm Up

24. Algebra 3 Chapter 10: Quadratic Relations and Conic Sections Lesson 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

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)