1. 1.What is the vertex for: 2.Describe the transformation: 3.What is the vertex for: Warm up Reflect, stretch 2, left 4, up 1

2. Quadratic Regression

3. Quadratic Model Is a quadratic function that represents a real data set. Models are useful for making estimates.

4. Quadratic Regression Last year, you used a calculator to perform linear regressions, exponential regressions, and made predictions using the models. You can apply a similar statistical method to make a quadratic model for a given data set using quadratic regression.

5. Coefficient of Determination R 2 Shows how well a quadratic function model fits the data. The closer R 2 is to 1, the better the fit.  Example, in a model with R 2  0.996 the quadratic model is a good fit.

6. Example 1: 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 12 ft. Diameter (ft) 4567 Cost $19.95$20.25$25.00$34.95

7. Example 1 Continued Step 1 Enter the data into two lists in the calculator. Step 2 Use the quadratic regression feature. 2 nd Data, 5:

8. Use the model to estimate the cost of the pool with a diameter of 12 ft. Step 3 Table 1: f(12) enter ANSWER: For a diameter of 12 ft, the model estimates a cost of about $156.29. Example 1 Continued

9. Film Run Times (16 mm) Diameter (in) Reel Length (ft) Run time (minutes) 5200 5.55 7400 11.12 9.25600 16.67 10.5800 22.22 12.251200 33.33 13.751600 45.25 Example 2 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.

10. Step 1 Enter the data into two lists in a calculator. Step 2 Use the quadratic regression feature. Example 2 Continued

11. Step 3 Table 1: f(8) enter ANSWER: For a diameter of 8 in., the model estimates the reel length to be about 446 ft. Example 2 Continued Use the model to estimate the reel length for an 8-inch-diameter film.

12. Write a quadratic function that fits the points (2, 0), (3, –2), and (5, –12). f ( x ) = – x 2 + 3 x – 2 Example 3

13. Practice Worksheets QUADRATIC REGRESSION

14. REVIEW SHEET TEST TOMORROW! Homework