Muh IkhwanSMA Negeri 3Semarang
QUADRATIC INEQUALITIESBy : Muh IkhwanSMA Negeri 3 Semarang
Using the characteristics and laws of quadratic Inequalities
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:
QUADRATIC INEQUALITIESConcept and Exercises(Exploration, Elaboration and Confirmation )Quiz Interactive Download :http://ikhwansmaga.wordpress.com/
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