1. Quadratics and Completing the
Square

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

18. Quadratics and the Discriminant

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

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

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

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

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

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

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

26. Quadratics and the Discriminant
  b 2  4ac
b 
vertex   , 
  Note: if   0, no x intercepts
 2a 4a    0, one x intercept
b     0, two x intercepts
zeroes 
2a
e.g. Sketch the parabola y  x 2  8 x  12
  82  4 112 
 16

27. Quadratics and the Discriminant
  b 2  4ac
b 
vertex   , 
  Note: if   0, no x intercepts
 2a 4a    0, one x intercept
b     0, two x intercepts
zeroes 
2a
e.g. Sketch the parabola y  x 2  8 x  12
  82  4 112 
 16
  8 ,  16 
 vertex   
 2 4

28. Quadratics and the Discriminant
  b 2  4ac
b 
vertex   , 
  Note: if   0, no x intercepts
 2a 4a    0, one x intercept
b     0, two x intercepts
zeroes 
2a
e.g. Sketch the parabola y  x 2  8 x  12
  82  4 112 
 16
  8 ,  16 
 vertex   
 2 4
  4, 4 

29. Quadratics and the Discriminant
  b 2  4ac
b 
vertex   , 
  Note: if   0, no x intercepts
 2a 4a    0, one x intercept
b     0, two x intercepts
zeroes 
2a
e.g. Sketch the parabola y  x 2  8 x  12
  82  4 112 
 16 Exercise 8B; 1cfi, 2bd, 3c, 4b, 6bei, 10b,
  8 ,  16  11d, 16, 17, 20*
 vertex   
 2 4
Exercise 8C; 1adg, 2adg, 3ad, 5ac, 8ac,
  4, 4  10, 13*