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Inverse Variation: Quadratic Functions and Graphing

Learn about inverse variation with quadratic functions and graphing tables of data. Identify inverse variation, determine the constant product, and graph the inverse variation functions.

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Inverse Variation: Quadratic Functions and Graphing

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  1. Inverse Variation 13-7 Course 3 Warm Up Problem of the Day Lesson Presentation

  2. Inverse Variation 13-7 4, 0, 9 1 4 4 Course 3 Warm Up Find f(–4), f(0), and f(3) for each quadratic function. 1.f(x) = x2 + 4 2.f(x) = x2 3.f(x) = 2x2 – x + 3 20, 4, 13 39, 3, 18

  3. Inverse Variation 13-7 Course 3 Problem of the Day Use the digits 1–8 to fill in 3 pairs of values in the table of a direct variation function. Use each digit exactly once. The 2 and 3 have already been used. 8 56 1 4 7

  4. Inverse Variation 13-7 Course 3 Learn to recognize inverse variation by graphing tables of data.

  5. Inverse Variation 13-7 Course 3 Insert Lesson Title Here Vocabulary inverse variation

  6. Inverse Variation 13-7 k x 120 x y= y= Course 3 An inverse variation is a relationship in which one variable quantity increases as another variable quantity decreases. The product of the variables is a constant. xy = 120 xy = k

  7. Inverse Variation 13-7 The relationship is an inverse variation: y = . 24 x Course 3 Additional Example 1A: Identify Inverse Variation Determine whether the relationship is an inverse variation. The table shows how 24 cookies can be divided equally among different numbers of students. 2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24 xy = 24 The product is always the same.

  8. Inverse Variation 13-7 Helpful Hint To determine if a relationship is an inverse variation, check if the product of x and y is always the same number. Course 3

  9. Inverse Variation 13-7 Course 3 Additional Example 1B: Identify Inverse Variation Determine whether each relationship is an inverse variation. The table shows the number of cookies that have been baked at different times. The product is not always the same. 12(15) = 180; 24(30) = 720 The relationship is not an inverse variation.

  10. Inverse Variation 13-7 The relationship is an inverse variation: y = . 60 x Course 3 Check It Out: Example 1A Determine whether the relationship is an inverse variation. 30(2) = 60; 20(3) = 60; 15(4) = 60; 12(5) = 60; 10(6) = 60 xy = 60 The product is always the same.

  11. Inverse Variation 13-7 Course 3 Check It Out: Example 1B Determine whether the relationship is an inverse variation. The product is not always the same. 2(4) = 8; 2(6) = 12 The relationship is not an inverse variation.

  12. Inverse Variation 13-7 4 x 12 12 – Course 3 Additional Example 2A: Graphing Inverse Variations Create a table. Then graph the inverse variation function. f(x) = –1 –2 –4 –8 8 4 2 1

  13. Inverse Variation 13-7 –1 x 12 12 – 1 3 1 2 – – Course 3 Additional Example 2B: Graphing Inverse Variations Create a table. Then graph the inverse variation function. f(x) = 1 3 1 2 1 2 –2 –1

  14. Inverse Variation 13-7 4 x 12 12 – Course 3 Check It Out: Example 2A Create a table. Then graph the inverse variation function. f(x) = – 1 2 4 8 –8 –4 –2 –1

  15. Inverse Variation 13-7 8 x Course 3 Check It Out: Example 2B Create a table. Then graph the inverse variation function. f(x) = –1 –2 –4 –8 8 4 2 1

  16. Inverse Variation 13-7 1500 x You can see from the table that xy = 5(300) = 1500, so y = . Course 3 Additional Example 3: Application As the pressure on the gas in a balloon changes, the volume of the gas changes. Find the inverse variation function and use it to find the resulting volume when the pressure is 30 lb/in2. If the pressure on the gas is 30 lb/in2, then the volume of the gas will be y = 1500 ÷ 30 = 50 in3.

  17. Inverse Variation 13-7 You can see from the table that xy = 10(20) = 200, so y = . 200 x Course 3 Check It Out: Example 3 An eighth grade class is renting a bus for a field trip. The more students participating, the less each student will have to pay. Find the inverse variation function, and use it to find the amount of money each student will have to pay if 50 students participate. If 50 students go on the field trip, the price per student will be y = 200  50 = $4.

  18. Inverse Variation 13-7 Course 3 Insert Lesson Title Here Lesson Quiz: Part I Tell whether each relationship is an inverse variation. 1. 2. yes no

  19. Inverse Variation 13-7 1 4x Course 3 Insert Lesson Title Here Lesson Quiz: Part II 3. Graph the inverse variation function f(x) = .

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