Maybank Islamic PETRONAS Ikhwan Visa Card-i Agreement The ...
Muh Ikhwan
description
Transcript of Muh Ikhwan
![Page 1: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/1.jpg)
Muh Ikhwan
SMA Negeri 3
Semarang
![Page 2: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/2.jpg)
QUADRATIC INEQUALITIES
By : Muh Ikhwan
SMA Negeri 3 Semarang
![Page 3: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/3.jpg)
Standard Competition
Using the characteristics and laws of quadratic Inequalities
![Page 4: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/4.jpg)
Indicator
Determining the solution set of quadratic inequalities by the graph
Determining the solution set of quadratic inequalities by number line
![Page 5: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/5.jpg)
Learning PrerequisitesLearning Prerequisites::Sketching the graph of the
corresponding quadratic expressions.Method of factorization.
Students will be able to solve the quadratic inequalities by graphical and number line method.
Aims and Objectives:Aims and Objectives:
![Page 6: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/6.jpg)
QUADRATIC INEQUALITIES
Concept and Exercises(Exploration, Elaboration and Confirmation )
Concept and Exercises(Exploration, Elaboration and Confirmation )
Quiz Interactive Quiz Interactive
Download :http://ikhwansmaga.wordpress.com/
Download :http://ikhwansmaga.wordpress.com/
![Page 7: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/7.jpg)
Method ofGraph
sketching
![Page 8: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/8.jpg)
Solve the quadratic inequality Solve the quadratic inequality xx2 2 – 5– 5x x + 6 > 0 graphically.+ 6 > 0 graphically.
![Page 9: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/9.jpg)
Procedures:
Step (2): we have y = (x – 2)(x – 3) ,i.e. y = 0, when x = 2 or x = 3
Factorize x2 – 5x + 6
The corresponding quadratic function is y = x2 – 5x + 6
Sketch the graph of y = x2 – 5x + 6
Step (1):
Step (3):
Step (4): Find the solution from the graph
![Page 10: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/10.jpg)
Sketch the graph Sketch the graph y =y = xx2 2 – 5– 5x x + 6 .+ 6 .
x
y
0
What is the solution of What is the solution of xx2 2 – 5– 5x x + 6 > + 6 > 0 0 ??
y = (x – 2)(x – 3) , y = 0, when x = 2 or x = 3.
2 3
![Page 11: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/11.jpg)
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
![Page 12: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/12.jpg)
x
y
0
When x < 2x < 2,the curve is
above the x-axisi.e., y > 0
x2 – 5x + 6 > 0
When x > 3x > 3,the curve is
above the x-axisi.e., y > 0
x2 – 5x + 6 > 0
2 3
![Page 13: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/13.jpg)
From the sketch, we obtain the solution
3xor2x
![Page 14: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/14.jpg)
By Number Line ?
![Page 15: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/15.jpg)
Number Line Solution:
0 2 3
3xor2x
![Page 16: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/16.jpg)
Solve the quadratic inequality Solve the quadratic inequality xx2 2 – 5– 5xx + 6 < 0. + 6 < 0.
Same method as example 1 !!!Same method as example 1 !!!
![Page 17: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/17.jpg)
x
y
0
When 2 < x < 32 < x < 3,the curve is
below the x-axisi.e., y < 0
x2 – 5x + 6 < 0
2 3
x2 – 5x + 6 < 0
![Page 18: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/18.jpg)
From the sketch, we obtain the solution
2 < x < 3
![Page 19: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/19.jpg)
0 2 3
Number Line Solution:
2 < x < 3
![Page 20: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/20.jpg)
Solve
Exercise 1:
.012 xx
x < –2 or x > 1
Answer:
x
y
00–2 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
![Page 21: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/21.jpg)
Solve
Exercise 2:
.0122 xx
–3 < x < 4
Answer:
x
y
00–3 4
Find the x-intercepts of the curve:Find the x-intercepts of the curve:
xx22 – 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
.0122 xx
![Page 22: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/22.jpg)
Solve
Exercise 3:
.107
22
xx
–7 < x < 5
Solution:
x
y
0
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
271022 xx
03522 xx
057 xx–7 5
![Page 23: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/23.jpg)
Solve
Exercise 4:
.3233 xxx
Solution:
x
y
0
35 22
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 23
0–3 23
x –3 or x 2/3
![Page 24: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/24.jpg)
Quiz interactive on line http://
www.classzone.com/etest/viewTestPractice.htm?testId=4293&seqNumber=4&testSessionId=null&startUrl=http://www.classzone.com/books/algebra_1/lessonquiz_national.cfm
![Page 25: Muh Ikhwan](https://reader035.fdocuments.us/reader035/viewer/2022062217/5681591d550346895dc644aa/html5/thumbnails/25.jpg)
THANK YOU