1 / 29

Chapter 2

Chapter 2 . 2-8 curve fitting with quadratic models. SAT Problem of the day. Three distinct positive integers have a sum of 15 and a product of 45.What is the largest of these integers? A)1 B)3 C)5 D)9 E)15. Solution to the SAT problem of the day. The right answer is D. Objectives .

palila
Download Presentation

Chapter 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2 2-8 curve fitting with quadratic models

  2. SAT Problem of the day • Three distinct positive integers have a sum of 15 and a product of 45.What is the largest of these integers? • A)1 • B)3 • C)5 • D)9 • E)15

  3. Solution to the SAT problem of the day • The right answer is D

  4. Objectives Use quadratic functions to model data. Use quadratic models to analyze and predict.

  5. Quadratic functions • Recall that you can use differences to analyze patterns in data. For a set of ordered parts with equally spaced x-values, a quadratic function has constant nonzero second differences, as shown below.

  6. Example#1 • Determine whether the data set could represent a quadratic function. Explain.

  7. Solution to Example#1 • Find the first and second differences. 1st 2 6 10 14 • 2nd 4 4 4 • Quadratic function: second differences are constant for equally spaced x-values

  8. Example#2 • Determine whether the data set could represent a quadratic function. Explain.

  9. Solution to Example#2 1st 2 6 18 5 2nd 4 12 36 Not a Quadratic function: second differences are not constant for equally spaced x-values

  10. Example#3 Determine whether the data set could represent a quadratic function. Explain.

  11. Solution to Example#3 1st 10 14 18 22 2nd 4 4 4 Quadratic function: second differences are constant for equally spaced x-values

  12. Student guided practice • Go to your book page 121and do problems 2 to 3

  13. Quadratic functions • Just as two points define a linear function, three non collinear points define a quadratic function. You can find three coefficients a, b, and c, of f(x) = ax2 + bx + c by using a system of three equations, one for each point. The points do not need to have equally spaced x-values.

  14. Example#4 • Write a quadratic function that fits the points (1, –5), (3, 5) and (4, 16). • Solution: • Use each point to write a system of equations to find a, b, and c in f(x) = ax2 + bx+ c.

  15. Example#5 • Write a quadratic function that fits the points (0, –3), (1, 0) and (2, 1).

  16. Student guided practice • Go to your book and do problems 5 and 6 from page 121

  17. QUADRATIC MODEL What is a quadratic model? A quadratic model is a quadratic function that represents a real data set. Models are useful for making estimates. In Chapter 2, you used a graphing calculator to perform a linear regression and make predictions. You can apply a similar statistical method to make a quadratic model for a given data set using quadratic regression.

  18. Example#6 • The table shows the cost of circular plastic wading pools based on the pool’s diameter. Find a quadratic model for the cost of the pool, given its diameter. Use the model to estimate the cost of the pool with a diameter of 8 ft.

  19. Example#6 solution • Step 1 Enter the data into two lists in a graphing calculator.

  20. Example#6 solution continue • Step 2 Use the quadratic regression feature. • Step 3 Graph the data and function model to verify that the model fits the data

  21. Example6 solution • Step 4 Use the table feature to find the function value x = 8.

  22. Example#6 solution • A quadratic model is f(x) ≈ 2.4x2 – 21.6x + 67.6, where x is the diameter in feet and f(x) is the cost in dollars. For a diameter of 8 ft, the model estimates a cost of about $49.54.

  23. Example#7 • The tables shows approximate run times for 16 mm films, given the diameter of the film on the reel. Find a quadratic model for the reel length given the diameter of the film. Use the model to estimate the reel length for an 8-inch-diameter film.

  24. Example#7

  25. Example#7 solution • Step 4 Use the table feature to find the function value x = 8. A quadratic model is L(d)  14.3d2 – 112.4d + 430.1, where d is the diameter in inches and L(d) is the reel length. For a diameter of 8 in., the model estimates the reel length to be about 446 ft.

  26. Student guided practice • Do problem 19 page 122 from book

  27. Homework • Do problems 11-18 from book page 121 and 122

  28. closure • Today we saw about fitting curve in a quadratic model • Next class we are going to continue with operations with complex numbers

  29. Have a nice day !!!!

More Related