Thurs – 15th Mar – Solving a quadratic that will not factorise

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
   
3. x² - 6x + 3
   
4. x² + 6x + 7
   
5. x² - 4x - 1
   
6. x² + 3x + 3
   
7. x² - 5x - 5
   
8. x² + x - 1
   
9. x² + 8x - 6
   
10. x² + 2x -1
    
11. x² - 2x - 7
    

    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.