1 / 46

Writing equations of conics in vertex form

Writing equations of conics in vertex form. MM3G2. Write the equation for the circle in vertex form :. Example 1 Step 1: Move the constant to the other side of the equation & put your common variables together. Example 1.

aure
Télécharger la présentation

Writing equations of conics in vertex form

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Writing equations of conics in vertex form MM3G2

  2. Write the equation for the circle in vertex form: • Example 1 Step 1: Move the constant to the other side of the equation & put your common variables together

  3. Example 1 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 1 so divide everything by 1

  4. Example 1 • Step 3: Group the x terms together and the y terms together using parenthesis.

  5. Example 1 • Step 4: Complete the square for the x terms Then for the y terms

  6. Example 1 • Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  7. Write the equation for the circle in vertex form: • Example 2 • Step 1: Move the constant to the other side of the equation & put your common variables together

  8. Example 2 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 2 so divide everything by 2

  9. Example 2 • Step 3: Group the x terms together and the y terms together using parenthesis.

  10. Example 2 • Step 4: Complete the square for the x terms Then for the y terms

  11. Example 2 • Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  12. Write the equation for the circle in vertex form: • Example 3 • Step 1: Move the constant to the other side of the equation & put your common variables together

  13. Example 3 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 4 so divide everything by 4

  14. Example 3 • Step 3: Group the x terms together and the y terms together using parenthesis.

  15. Example 3 • Step 4: Complete the square for the x terms Then for the y terms

  16. Example 3 Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  17. Write the equation for the circle in vertex form: • Example 4 • Step 1: Move the constant to the other side of the equation & put your common variables together

  18. Example 4 • Step 2: Identify the coefficients of the squared terms and divide everything by that coefficient. • Both coefficients are 5 so divide everything by 5

  19. Example 4 • Step 3: Group the x terms together and the y terms together using parenthesis.

  20. Example 4 • Step 4: Complete the square for the x terms Then for the y terms

  21. Example 4 • Step 5: Write the factored form for the groups. What is the center of this circle? What is the radius?

  22. Recall: • The equation for a circle does not have denominators • The equation for an ellipse and a hyperbola do have denominators • The equation for a circle is not equal to one • The equation for an ellipse and a hyperbola are equal to one • We have a different set of steps for converting ellipses and hyperbolas to the vertex form:

  23. Write the equation for the ellipse in vertex form: • Example 5 • Step 1: Move the constant to the other side of the equation and move common variables together

  24. Example 5 • Step 2: Group the x terms together and the y terms together • Step 3: Factor the GCF (coefficient)from the x group and then from the y group

  25. Example 5 • Step 4: Complete the square on the x group (don’t forget to multiply by the GCF before you add to the right side.) Then do the same for the y terms

  26. Example 5 • Step 5: Write the factored form for the groups. **Now we have to make the equation equal 1 and that will give us our denominators

  27. Example 5 • Step 6: Divide by the constant.

  28. Example 5 • Step 7: simplify each fraction. Now the equation looks like what we are used to!! 1 4 9

  29. What is the center of this ellipse? • What is the length of the major axis? • What is the length of the minor axis?

  30. Example 6: Ellipse Step 1: Step 2: Step 3:

  31. Example 6 Step 4: Step 5:

  32. Example 6 Step 6: 1 4 25

  33. What is the center of this ellipse? • What is the length of the major axis? • What is the length of the minor axis?

  34. Example 7: Ellipse Step 1: Step 2: Step 3:

  35. Example 7 Step 4: Step 5:

  36. Example 7 Step 6: 1 81 36

  37. What is the center of this ellipse? • What is the length of the major axis? • What is the length of the minor axis?

  38. Example 8: Hyperbola Step 1: Step 2: Step 3:

  39. Example 8 Step 4: Step 6:

  40. Example 8 Step 6: 1 2

  41. What is the center of this hyperbola? • What is the length of the transverse axis? • What is the length of the conjugate axis?

  42. Example 9: Hyperbola Step 1: Step 2: Step 3:

  43. Example 9 Step 4: Step 5:

  44. Example 9 Step 6: 1 9 4

  45. What is the center of this hyperbola? • What is the length of the transverse axis? • What is the length of the conjugate axis?

  46. You Try! • Write the equation of each conic section in vertex form: Identify the center of each conic section as well as the length of the major/minor or transverse/conjugate axis.

More Related