1. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models For a set of ordered pairs with equally spaced x- values, a quadratic function has constant nonzero second differences, as shown below.

2. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Determine whether the data set could represent a quadratic function. Explain. Example 1B: Identifying Quadratic Data x 34567 y 1392781 Not a Quadratic function: second differences are not constant for equally spaced x-values 2nd 4 12 36 1st 2 6 18 54 x 34567 y 1392781 Equally spaced x-values Find the first and second differences.

3. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models 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. Example 3: Consumer Application Diameter (ft)4567 Cost$19.95$20.25$25.00$34.95

4. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Example 3 Continued Step 1 Enter the data into two lists in a graphing calculator. Step 2 Use the quadratic regression feature.

5. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Example 3 Continued Step 3 Graph the data and function model to verify that the model fits the data. Step 4 Use the table feature to find the function value x = 8.

6. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Example 3 Continued A quadratic model is f(x) ≈ 2.4x 2 – 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.

7. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Year AIDS Cases 199941,356 200041,267 200140,833 200241,289 200343,171 The table below lists the total estimated numbers of AIDS cases, by year of diagnosis from 1999 to 2003 in the United States (Source: US Dept. of Health and Human Services, Centers for Disease Control and Prevention, HIV/AIDS Surveillance, 2003.) Use the model to predict the number of AIDS cases in the year 2006.

8. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Example 3 Continued Step 1 Enter the data into two lists in a graphing calculator. Let the year 1998 represent t = 0. Step 2 Use the quadratic regression feature. We let 1998 be when t = 0 because it allows for a more accurate approximation of the quadratic function. The quadratic regression’s coefficients of a, b, and c will be more accurate when there isn’t 2000 units separating the y-axis and the first data point.

9. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Example 3 Continued Step 3 Graph the data and function model to verify that the model fits the data. Step 4 Use the table feature to find the function value x = 8.

10. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models Example 3 Continued A quadratic model is f(t) ≈ 345.143t 2 – 1705.657t + 42903, where x is the number of years after 1998 and f(t) is the amount of AIDS cases. For the year 2006, the model estimates the number of AIDS cases to be 51,347.

11. Holt Algebra 2 5-8 Curve Fitting with Quadratic Models HW pg. 377 #12-14,19,24,25,26,36,38,41,50