BAHAN AJAR MODUL pp_pertdkuadrat.ppt

MATH

1. The Chinese University of
Hong Kong
EDD 5161R99EDD 5161R99
Group ProjectGroup Project
Chan Kwok Ping (S98118370)
Seto Fung Mei (S98038260)

2. Form 5 --- lecturing

3. Learning PrerequisitesLearning Prerequisites::
Sketching the graph of the corresponding
quadratic expressions.
Method of factorization.
Basic knowledge of Rectangular coordinate plane.
Students will be able to solve the quadratic
inequalities by graphical method.
Represent the solutions graphically.
Aims and Objectives:Aims and Objectives:

4. ContentContent
History (1) Sign of inequality
(2) Godfrey Harold Hardy
Inequality & Coordinate Plane
Solving Quadratic Inequality by Method of Graph
Sketching
Exercise

5. Method of
Graph sketching

6. Solve the quadratic inequality Solve the quadratic inequality
xx
2 2
– 5– 5x x + 6 > 0 graphically.+ 6 > 0 graphically.

7. Procedures:
Step (2):
we have y = (x – 2)(x – 3) ,
i.e. y = 0, when x = 2 or x = 3.
Factorize x
2
– 5x + 6,
The corresponding quadratic function is
y = x
2
– 5x + 6
Sketch the graph of y = x
2
– 5x + 6.
Step (1):
Step (3):
Step (4): Find the solution from the graph.

8. Sketch the graph Sketch the graph y =y = xx
2 2
– 5– 5x x + 6 .+ 6 .
x
y
0
6 5
2
  x x y
What is the solution of What is the solution of xx
2 2
– 5– 5x x + 6 > 0 + 6 > 0 ??
y = (x – 2)(x – 3) ,
 y = 0, when x = 2 or x = 3.

2 3

9. above the x-axis.so we choose the portion
x
y
0
We need to solve x
2
– 5x + 6 > 0,
The portion of the
graph above the x-axis
represents y > 0
(i.e. x
2
– 5x + 6 > 0)
The portion of the
graph below the x-axis
represents y < 0
(i.e. x
2
– 5x + 6 < 0)
2 3

10. x
y
0
When x < 2x < 2,
the curve is
above the x-axis
i.e., y > 0
x
2
– 5x + 6 > 0
When x > 3x > 3,
the curve is
above the x-axis
i.e., y > 0
x
2
– 5x + 6 > 0
2 3
65
2
 xxy

11. From the sketch, we obtain the solution

3xor2x

12. Graphical Solution:
0 2 3

13. Solve the quadratic inequality Solve the quadratic inequality
xx
2 2
– 5– 5xx + 6 < 0 graphically. + 6 < 0 graphically.
Same method as example 1 !!!Same method as example 1 !!!

14. x
y
0
6 5
2
  x x y
When 2 < x < 32 < x < 3,
the curve is
below the x-axis
i.e., y < 0
x
2
– 5x + 6 < 0
2 3

15. From the sketch, we obtain the solution

2 < x < 3

16. 0 2 3
Graphical Solution:

17. Solve
Exercise 1:
.012 xx
x < –2 or x > 1
Answer:
x
y
0
1 2  x x y
0–2 1
Find the x-intercepts of the Find the x-intercepts of the
curve:curve:
(x + 2)(x – 1)=0(x + 2)(x – 1)=0
x = –2 or x = 1x = –2 or x = 1
–2 1

18. Solve
Exercise 2:
.012
2
xx
–3 < x < 4
Answer:
x
y
0
12
2
  x x y
0–3 4
Find the x-intercepts of the curve:Find the x-intercepts of the curve:
xx
22
– x – 12 = 0 – x – 12 = 0
(x + 3)(x – 4)=0(x + 3)(x – 4)=0
x = –3 or x = 4x = –3 or x = 4
–3 4

19. Solve
Exercise 3:

.10
7
22

xx
–7 < x < 5
Solution:
x
y
0
35 2
2
  x x y
0–7 5
Find the x-intercepts of the Find the x-intercepts of the
curve:curve:
(x + 7)(x – 5)=0(x + 7)(x – 5)=0
x = –7 or x = 5x = –7 or x = 5

10
7
22

xx
27102
2
xx
0352
2
xx
057 xx
–7 5

20. Solve
Exercise 4:
.3233  xxx
Solution:
x
y
0
35 2
2
  x x y
Find the x-intercepts of the Find the x-intercepts of the
curve:curve:
(x + 3)(3x – 2)=0(x + 3)(3x – 2)=0
x = –3 or x = 2/3x = –3 or x = 2/3
3233  xxx
03233  xxx
 0233  xx
–3 2
3
0–3 2
3
x  –3 or x 
2/3

22. y
x
originO
x - axis
x P( x , y )
The horizontal number line
is called the x-axis.
The vertical number line
is called the y-axis.
y - axis
The point of intersection of
the axes is called the origin O.
y
Any point P on the plane is described by
two numbers x and y called coordinates.

23. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
( 3, 1 )A
( 4, 3 )B
( 1, 2 )C
( 2, 5 )D
What are the sign of the x- and
y-coordinates of A,B,C and D?
(+,+)

24. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(+,+)
E(4, 4 )
(3, 1 )F
(1, 2 )G
(2, 3 )H
What are the sign of the x- and
y-coordinates of E,F,G and H?
(,+)

25. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(,+) (+,+)
I(4,2 )
(3, 5 )L
(1, 3)K
(2,1)J
What are the sign of the x- and
y-coordinates of I,J,K and L?
(,)

26. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(,+) (+,+)
(,)
What are the sign of the x- and
y-coordinates of M,N,P and Q?
( 3,5 )Q
( 4,3 )
( 1,4 )M
( 2,1 )N
P (+,)

27. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(,+) (+,+)
(,) (+,)
Shade the part that y>0y>0 (i.e.”++”).

28. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(,+) (+,+)
(,) (+,)
Shade the part that y<0y<0 (i.e.””).

29. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(,+) (+,+)
(,) (+,)
Shade the part that x>0x>0 (i.e.”++”).

30. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
(,+) (+,+)
(,) (+,)
Shade the part that x<0x<0 (i.e.””).

31. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that x<x<11.

32. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that x<2x<2.

33. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that x>1x>1.

34. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that 2<x<12<x<1.

35. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that 3<x<23<x<2.

36. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that xx<<2 or x>12 or x>1.

37. 5
4
3
2
1
-4 -3 -2 -1 0 1 2 3 4

-1
-2
-3
-4
x
y
Shade the part that xx<<1 or x>41 or x>4.