1. MAT 150 Unit 2-4 Part 1: Quadratic Models

2. Objectives
Find the exact quadratic function that fits three points on a parabola
Model data approximately using quadratic functions

3. Example
A parabola passes through the points (0, 5), (4, 13), and (–2, 25). Write the equation of the quadratic function whose graph is this parabola. Solution

4. Example (cont) Solution
A parabola passes through the points (0, 5), (4, 13), and (–2, 25). Write the equation of the quadratic function whose graph is a parabola.
Solution

5. Example
A parabola passes through the points (0, 5), (4, 13), and (–2, 25). Write the equation of the quadratic function whose graph is a parabola.
Solution

6. Example
The table shows the dollar value or projected dollar value of the U.S. mobile Internet advertising market for the years from 2006 to 2012.

7. Example (cont)
a. Create a scatter plot of the data with x equal to the number of years after Solution

8. Example (cont)
b. Find the quadratic function that is the best fit for the data, with x equal to the number of years after Solution

9. Example (cont)
c. Graph the aligned data and the model on the same axes. Does this model seem like a reasonable fit? Solution

10. Example (cont)
d. Use the model to find the year in which the mobile Internet advertising market is projected to reach $3 billion. Solution

11. Example
The table gives the number of Starbucks stores in the United States for the years 1992 through 2009

12. Example (cont)
a. Create a scatter plot of the data points with x equal to the number of years after Solution

13. Example (cont)
b. Create a quadratic function that models the data, using the number of years after 1990 as the input x. Solution

14. Example (cont)
c. Graph the aligned data and the quadratic function on the same axes. Does the model seem like a reasonable fit? Solution

15. Example (cont)
d. Use the model to estimate the number of stores in Discuss the reliability of this estimate. Solution

16. Example (cont)
Use the model to estimate the number of stores in Discuss the reliability of this estimate.
Solution