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
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 4 112
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 4 112
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 4 112
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 4 112
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*