Tuesday, 17 April 2012

Weds 18th Apr – Solving quadratic Equations that do not factorise – Completing the square Method

LEARNING OBJECTIVE: Discover other methods of solving quadratics when they will not factorise

SUCCESS CRITERIA: You will be able to solve quadratics that do not factorise.

ENGAGEMENT ACTIVITIES:

Can You expand these equations

  1. (x+2)2
  2. (x-4)2
  3. (x+5)2
  4. (x- 3)2
  5. (x+1.5)2
  6. (x – 3.5)2

LESSON

Look at the following quadratics,

  1. Can you factorise them?
  2. If no, can you guess a solution using trial and improvement methods?

x2 + 4x – 8 = 0

x2 - 8x – 4 = 0


  1.  Look at (x+2)2 and the expression x2 + 4x + 2 –

    How are they different?

    What can we do to make this equation balance correctly?

    (x+2)2 = x2 + 4x + 2

    Examples

    1. x2 + 8x - 7
    2. x2 - 14x - 11
    3. x2 + 7x - 4

    Can you write the following equations in this form

    (x + a)2 –b or (x - a)2 –b

  2. x2 + 14x – 1 = (x+7) 2- 50
  3. x2 - 6x + 3 = (x-3) 2 -6
  4. x2 + 6x + 7 = (x+3) 2 -2
  5. x2 - 4x – 1 = (x-2) 2 -5
  6. x2 + 3x + 3 = (x + 1.5) 2+0.75
  7. x2 - 5x – 5 = (x-2.5) 2 -11.25
  8. x2 + x – 1 = (x+0.5) 2 -1.25
  9. x2 + 8x – 6 = (x+4) 2 -22
  10. x2 + 2x -1 = (x+1) 2 -2
  11. x2 - 2x – 7 = (x-1) 2 -8

    Look at these pairs of equations, can you complete the square and then solve the equations (leave your answer in surd form)

  12. x2 + 14x – 5 = 0 , (x + 7)2
  13. x2 -6x + 3 = 0 ,(x - 3)2
  14. x2 +6x + 7 = 0 ,(x + 3)2
  15. x2 - 4x - 1 = 0 ,(x - 2)2
  16. x2 + 3x + 3 = 0 ,(x + 1½ )2
  17. x2 - 5x – 5 = 0 ,(x - 3)2
  18. x2 + x - 1 = 0 ,(x + ½)2
  19. x2 + 8x - 6 = 0 ,(x + 4)2
  20. x2 + 2x -1 = 0 ,(x + 1)2
  21. x2 -2x - 7 = 0 ,(x - 1)2
     

PLENARY: Checking answers, stopping class and going over problems when stuck.
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