Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 164.3 Quadratic Functions and Their PropertiesChapter 4 Section 3: Quadratic Functions and Their PropertiesIn this section, we will…Graph quadratic functions using transformationsIdentify the axis of symmetry, vertex and intercepts of a quadratic functionDetermine if a quadratic function opens up or downIdentify the domain and range of a quadratic functionFind the minimum or maximum of a quadratic functionDetermine where a quadratic function is increasing, decreasing or constant over its domainSolve applications of quadratic functionsA quadratic function in General Form is a function of the form:2( )f x ax bx c= + +4.3 Quadratic Functions and Their PropertiesA quadratic function in Vertex Form is a function of the form:( )2( )f x a x h k= - +Example: 2( ) 3 5 2g x x x= + -Example:• If a > 0, then• If a < 0, then• What is the vertex of the parabola?( )2( ) 3 2 5h x x= - +4.3 Quadratic Functions and Their Properties214( ) 1f x x= +Example: Graph using transformations on the base function. base function:transformations:What is the coordinate of the vertex?4.3 Quadratic Functions and Their Properties2( ) 6 1f x x x= - -Example: Graph using transformations on the base function. base function:transformations:What is the coordinate of the vertex?4.3 Quadratic Functions and Their PropertiesFor each quadratic function, we will identify the following features algebraically:4.3 Quadratic Functions and Their PropertiesFor each quadratic function, we will identify the following features on the TI:4.3 Quadratic Functions and Their Properties2( ) ( 4) 5f x x= - -Example: Answer each of the following algebraically for• Will the graph open up or down? Explain.• Find the intercepts, axis of symmetry and vertex algebraically. x-intercept(s): y-intercept(s) axis of symmetry: vertex:4.3 Quadratic Functions and Their PropertiesExample: Graph ; label the intercepts, axis of symmetry and vertex.Determine the domain and range of the function. domain: range:Determine where the function is increasing and decreasing. increasing: decreasing:2( ) ( 4) 5f x x= - -Rework the last two slides using the TI.4.3 Quadratic Functions and Their Properties2( ) 6 9f x x x= + +Example: Answer each of the following algebraically for• Will the graph open up or down? Explain.• Find the intercepts, axis of symmetry and vertex algebraically. x-intercept(s): y-intercept(s) axis of symmetry: vertex:4.3 Quadratic Functions and Their PropertiesExample: Graph ; label the intercepts, axis of symmetry and vertex.Determine the domain and range of the function. domain: range:Determine where the function is increasing and decreasing. increasing: decreasing:Rework the last two slides using the TI.2( ) 6 9f x x x= + +4.3 Quadratic Functions and Their Properties2( ) 3 3 2g x x x=- + -Example: Answer each of the following algebraically for• Will the graph open up or down? Explain.• Find the intercepts, axis of symmetry and vertex algebraically. x-intercept(s): y-intercept(s) axis of symmetry: vertex:4.3 Quadratic Functions and Their PropertiesExample: Graph ; label the intercepts, axis of symmetry and vertex.Determine the domain and range of the function. domain: range:Determine where the function is increasing and decreasing. increasing: decreasing:Rework the last two slides using the TI.2( ) 3 3 2g x x x=- + -How to Solve a Word Problem:Step 1: Read the problem until you understand it. • What are we asked to find? • What information is given?• What vocabulary is being used?Step 2: Assign a variable to represent what you are looking for. Express any remaining unknown quantities in terms of this variable.Step 3: Make a list of all known facts and form an equation or inequality to solve. It may help to make a labeled: diagram, table or chart, graphStep 4: SolveStep 5: State the solution in a complete sentence by mirroring the original question. Be sure to include units when necessary.Step 6: Check your result(s) in the words of the problem• Does your solution make sense?4.3 Quadratic Functions and Their PropertiesExample: The John Deere Company has found that the revenue R, in dollars, from sales of heavy-duty tractors is a function of the unit price p, in dollars, that it charges:• Sketch the function in an appropriate viewing window; include your viewing window.• What unit price should be established for John Deere to maximize revenue?• What is the maximum revenue?2( ) 4 4000R p p p=- +4.3 Quadratic Functions and Their PropertiesExample: The function models the percentage of total income that an individual who is x years of age spends on total health care annually.• Sketch the function in an appropriate viewing window; include your viewing window.• Use the model to approximate the percentage of total income an individual who is 45 spends on health care annually?• At what age is the percentage of total income spent on health care 10%?• Describe what happens to the percentage of total income spent on health care as individuals age.2( ) 0.004 0.197 5.406H x x x= - +4.3 Quadratic Functions and Their PropertiesIndependent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved each problem; rework all problems that are incorrect.Read pages 293-301Homework: pages 302-305 #25, 27, 31, 41-49 odds, 61, 63, 81, 83, 874.3 Quadratic Functions and Their