1. The Sign Of A Quadratic

2. The Sign Of A Quadratic
Positive Definite
y
x

3. The Sign Of A Quadratic
Positive Definite
y
x

4. The Sign Of A Quadratic
Positive Definite
y
x
a0 , 0

5. The Sign Of A Quadratic
Positive Definite Negative Definite
y y
x x
a0 , 0

6. The Sign Of A Quadratic
Positive Definite Negative Definite
y y
x x
a0 , 0

7. The Sign Of A Quadratic
Positive Definite Negative Definite
y y
x x
a0 , 0 a0 , 0

8. Indefinite

9. Indefinite
y
x

10. Indefinite
y
x
a0 , 0

11. Indefinite
y y
x x
a0 , 0

12. Indefinite
y y
x x
a0 , 0 a0 , 0

13. Indefinite
y y
x x
a0 , 0 a0 , 0
y
x

14. Indefinite
y y
x x
a0 , 0 a0 , 0
y
x
a0 , 0

15. Indefinite
y y
x x
a0 , 0 a0 , 0
y y
x x
a0 , 0

16. Indefinite
y y
x x
a0 , 0 a0 , 0
y y
x x
a0 , 0 a0 , 0

17. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite

18. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0

19. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0
k 0

20. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0 0
k 0

21. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0 0
k 0 36  4k 2  0

22. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0 0
k 0 36  4k 2  0
k2  9

23. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0 0
k 0 36  4k 2  0
k2  9
k  3 or k  3

24. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0 0
k 0 36  4k 2  0
k2  9
k  3 or k  3
k  3

25. e.g. Find the values of k which makes kx 2  6 x  k  0 positive definite
a0 0
k 0 36  4k 2  0
k2  9
k  3 or k  3
k  3
Exercise 8G; 2ace, 3bd, 4bd, 5bd, 6, 12, 15, 17*