1. Quadratics and Completing the
Square

2. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  

3. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  

4. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  

5. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  

6. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts

7. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   

8. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  

9. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
4 2
4 2
x
x
  
  

10. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
4 2
4 2
x
x
  
  

11. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  

12. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)

13. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  

14. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  

15. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
9 3
1
3
k
k
 
 

16. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
9 3
1
3
k
k
 
 
  21
5 3
3
y x   

17. Quadratics and Completing the
Square
e.g. 2
Sketch the parabola 8 12y x x  
2
8 12y x x  
 
2
4 4x  
 vertex is 4, 4  
x intercepts  
2
4 4 0x   
 
2
4 4x  
6 or 2x x   
   
intercepts are
6,0 and 2,0
x
 
4 2
4 2
x
x
  
  
(ii) Write down the quadratic with roots 2 and 8 and vertex (5,3)
  2
5 3y k x  
    2
2,0 : 0 2 5 3k  
9 3
1
3
k
k
 
 
  21
5 3
3
y x   
 21
10 16
3
y x x   

18. Quadratics and the Discriminant

19. Quadratics and the Discriminant
2
4b ac  

20. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 

21. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  


22. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 

23. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 

24. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 

25. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
2
e.g. Sketch the parabola 8 12y x x  

26. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  

27. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
8 16
vertex ,
2 4
     
 

28. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
8 16
vertex ,
2 4
     
 
 4, 4  

29. Quadratics and the Discriminant
2
4b ac  
vertex ,
2 4
b
a a
    
 
zeroes
2
b
a
  

Note: if 0, no interceptsx 
0, one interceptx 
0, two interceptsx 
  2
8 4 1 12
16
  

2
e.g. Sketch the parabola 8 12y x x  
8 16
vertex ,
2 4
     
 
 4, 4  
Exercise 8B; 1cfi, 2bd, 3c, 4b, 6bei, 10b,
11d, 16, 17, 20*
Exercise 8C; 1adg, 2adg, 3ad, 5ac, 8ac,
10, 13*