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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

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Muh Ikhwan

SMA Negeri 3

Semarang

By : Muh Ikhwan

SMA Negeri 3 Semarang

Standard Competition
• Using the characteristics

Inequalities

Indicator
• Determining the solution set of quadratic inequalities by the graph
• Determining the solution set of quadratic inequalities by number line
Learning Prerequisites:

Students will be able to solve the quadratic inequalities by graphical and number line method.

Aims and Objectives:

Sketching the graph of the corresponding quadratic expressions.

Method of factorization.

Concept and Exercises

(Exploration, Elaboration and Confirmation )

Quiz Interactive

http://ikhwansmaga.wordpress.com/

Example 1:

Solve the quadratic inequality x2 – 5x + 6 > 0 graphically.

Procedures:

Step (1):

The corresponding quadratic function is y = x2 – 5x + 6

Step (2):

Factorize x2 – 5x + 6

we have y = (x – 2)(x – 3) ,i.e. y = 0, when x = 2 or x = 3

Step (3):

Sketch the graph of y = x2 – 5x + 6

Step (4):

Find the solution from the graph

y

y = (x – 2)(x – 3) , y = 0, when x = 2 or x = 3.

x

0

2

3

Sketch the graph y =x2 – 5x + 6 .

What is the solution of x2 – 5x + 6 > 0 ?

so we choose the portion

above the x-axis.

2

3

We need to solve x 2 – 5x + 6 > 0,

y

The portion of the graph above the x-axis represents y > 0

(i.e. x 2 – 5x + 6 > 0)

x

0

The portion of the graph below the x-axis represents y < 0

(i.e. x 2 – 5x + 6 < 0)

2

3

y

When x < 2,

the curve is

above the x-axis

i.e., y > 0

x2 – 5x + 6 > 0

When x > 3,

the curve is

above the x-axis

i.e., y > 0

x2 – 5x + 6 > 0

x

0

or

From the sketch, we obtain the solution

or

2

0

3

Number Line Solution:

Example 2:

Solve the quadratic inequality x2 – 5x + 6 < 0.

Same method as example 1 !!!

2

3

y

x2 – 5x + 6 < 0

x

0

When 2 < x < 3,

the curve is

below the x-axis

i.e., y < 0

x2 – 5x + 6 < 0

2

0

3

Number Line Solution:

2 < x < 3

SolveExercise 1:

y

x

0

1

–2

–2

0

1

Find the x-intercepts of the curve:

(x + 2)(x – 1)=0

x = –2 or x = 1

x < –2 or x > 1

SolveExercise 2:

y

x

0

4

–3

–3

0

4

Find the x-intercepts of the curve:

x2 – x – 12 = 0

(x + 3)(x – 4)=0

x = –3 or x = 4

–3 < x < 4

y

x

0

5

–7

0

–7

5

Find the x-intercepts of the curve:

(x + 7)(x – 5)=0

x = –7 or x = 5

Exercise 3:

Solve

Solution:

–7 < x < 5

y

x

0

2

3

–3

0

–3

2

3

Find the x-intercepts of the curve:

(x + 3)(3x – 2)=0

x = –3 or x = 2/3

Exercise 4:

Solve

Solution:

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