Muh Ikhwan

SMA Negeri 3

Semarang

QUADRATIC INEQUALITIES

By : Muh Ikhwan

SMA Negeri 3 Semarang

Standard Competition

Using the characteristics and laws of quadratic Inequalities

Indicator

Determining the solution set of quadratic inequalities by the graph

Determining the solution set of quadratic inequalities by number line

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:

QUADRATIC INEQUALITIES

Concept and Exercises(Exploration, Elaboration and Confirmation )

Concept and Exercises(Exploration, Elaboration and Confirmation )

Quiz Interactive Quiz Interactive

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Download :http://ikhwansmaga.wordpress.com/

Method ofGraph

sketching

Solve the quadratic inequality Solve the quadratic inequality xx2 2 – 5– 5x x + 6 > 0 graphically.+ 6 > 0 graphically.

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

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

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

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

From the sketch, we obtain the solution

3xor2x

By Number Line ?

Number Line Solution:

0 2 3

3xor2x

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 !!!

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

From the sketch, we obtain the solution

2 < x < 3

0 2 3

Number Line Solution:

2 < x < 3

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

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

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

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

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

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