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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 - PowerPoint PPT Presentation

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• Muh IkhwanSMA Negeri 3Semarang

• QUADRATIC INEQUALITIESBy : Muh IkhwanSMA 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 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:

• Method of Graph sketching

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

• Procedures: Step (2): we have y = (x 2)(x 3) , i.e. y = 0, when x = 2 or x = 3Factorize x2 5x + 6The corresponding quadratic function is y = x2 5x + 6 Sketch the graph of y = x2 5x + 6Step (1):Step (3):Step (4): Find the solution from the graph

• Sketch the graph y = x2 5x + 6 .What is the solution of x2 5x + 6 > 0 ?

• xy0We 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)

• xy0When x < 2,the curve isabove the x-axisi.e., y > 0x2 5x + 6 > 0When x > 3,the curve isabove the x-axisi.e., y > 0x2 5x + 6 > 0

• From the sketch, we obtain the solution

• By Number Line ?

• Number Line Solution:

• Solve the quadratic inequality x2 5x + 6 < 0.Same method as example 1 !!!

• xy0When 2 < x < 3,the curve isbelow the x-axisi.e., y < 0x2 5x + 6 < 0x2 5x + 6 < 0

• From the sketch, we obtain the solution 2 < x < 3

• Number Line Solution:2 < x < 3

• SolveExercise 1:x < 2 or x > 1Answer:Find the x-intercepts of the curve:(x + 2)(x 1)=0x = 2 or x = 1

• SolveExercise 2:3 < x < 4Answer:Find the x-intercepts of the curve:x2 x 12 = 0(x + 3)(x 4)=0x = 3 or x = 4

• SolveExercise 3:7 < x < 5Solution:Find the x-intercepts of the curve:(x + 7)(x 5)=0x = 7 or x = 5

• SolveExercise 4:Solution:Find the x-intercepts of the curve:(x + 3)(3x 2)=0x = 3 or x = 2/3x 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

• THANK YOU

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