Muh Ikhwan

  • View
    38

  • Download
    4

Embed Size (px)

DESCRIPTION

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

Text of Muh Ikhwan

  • 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:

  • 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

  • THANK YOU

    *