1. Warm Up 1. Please have your homework and tracking sheet out and ready for me when I get to you.   a. Find the line of best fit for these data. _______________________   b. What is the correlation coefficient for these data to the nearest hundredth?______________________   c. Based on these data what might the number of twins’ births be expected to be in 1997?   d. Actually in 1997, there were 104,137 sets of twins born. What does this mean about the line of best fit? What might explain this discrepancy?

2. Homework Answers

4. Next Week  Review Monday  Test Tuesday  I WILL be available for make up and tutoring after school on Monday since the test is on Tuesday.

5. Review 2: List the intervals where the Graph is increasing. List the intervals where the Graph is decreasing. What is the limit as “x” Approaches infinity? What is the limit as “x” Approaches -infinity?

6. You Do 16 (1, 18) List the intervals where the Graph is increasing. List the intervals where the Graph is decreasing. What is the limit as “x” Approaches infinity? What is the limit as “x” Approaches -infinity?

7. Standard Form  Vertex Form  What is the vertex form of y = 2x 2 + 10x + 7 ?  You may either complete the square or use your calculator.

8. You Do  Write the function in vertex form. y = x 2 – 4x + 6

9. Quick Check 1. In your own words, define vertex, zeroesand axis of symmetry of a parabola. 1. Find the vertex and zeros of y = 3x 2 – 4x – 2

10. Quadratic Regression   What is the difference between a quadratic function and a quadratic regression?

11. QuadReg   1. STAT: edit.   2. Enter the values of the _____________ variable in L 1.   3. Enter the values of the _____________ variable in L 2.   4. Make sure your calculator is set to_______________ so that you can observe the ______________ _____________, and determine how good a fit your model is.   5. 2 nd : Y=   6. Turn on the first STAT Plot   7. STAT  CALC   8. QuadReg (number ____).

12. R2R2   Instead of an r value, quadratic regressions have an r 2. R 2 tells us :   What percentage of the time the model will be a good fit for the data.

13. Cigarette Consumption   a. Create the scatterplot for this data. Notice how the plot seems to __________ rapidly and then ________ _______ before cigarette consumption begins to fall off.   b. What is the quadratic regression for this data?   c. What is the r 2 value? How good a model is this? US Cigarette consumption

14. Cont….   d. When did consumption from the most rapidly? What events in history might account for this steep increase?   e. When does the consumption drop? Why?

15. Quadratic vs. Linear Regression  I use LINEAR when my y-values seem to consistently INCREASE OR DECREASE  I use QUADRATIC when my y-values seem to INCREASE AND THEN DECREASE (or vice versa)

16. The Chesapeake Bay

18. Average Monthly Temperatures of the Chesapeake Bay MonthJanFebMarAprMayJunJulAugSepOctNovDec Temp313444546472767568574736 a. What is the independent variable? b. What is the dependent variable? c. Enter your data in L 1 and L 2. Look at the scatterplot. d. Talk with the person sitting next to you about what the window should be: ･ xmin: Xmin=______ ･ xmax: Xmax=______ ･ ymin: Ymin=______ ･ ymax: Ymax=______

19. Cont…   e. What is the quadratic regression equation?   f. What is r 2 ? What does this number tell us?   g. According to the model, in what month is the temperature the highest?   h. During what month(s) would the temperature by 50?

20. Analysis  According to the model, what month does the maximum temperature occur?  According to the model, during what months would the temperature be 50°? June! March and October

21. Darryl is standing on top of the bleachers and throws a football across the field. The data that follows gives the height of the ball in feet versus the seconds since the ball was thrown.Time0.20.611.21.522.52.83.43.84.5Ht.921101301341421441401321129044 a. a. Show a scatter plot of the data. What is the independent variable, and what is the dependent variable? b. b. What prediction equation (mathematical model) describes this data? c. c. When will the ball be at a height of 150 feet? d. d. When will the ball be at a height of 100 feet? e. e. At what times will the ball be at a height greater than 100 feet? f. f. When will the ball be at a height of 40 feet? g. g. When will the ball hit the ground?

22. a. Show a scatter plot of the data. What is the independent variable, and what is the dependent variable? Independent variable (x): Time! (always!) Dependent variable (y): Height

23. b. What prediction equation (mathematical model) describes this data? QUADRATIC!!

24. c. When will the ball be at a height of 150 feet? Height (y) Height (y) Put 150 in y2. Put 150 in y2. What happened?!? Explain.

25. d. When will the ball be at a height of 100 feet? Put 100 in y2 and find the intersection! Put 100 in y2 and find the intersection!.34 seconds and 3.65 seconds

26. e. At what times will the ball be at a height greater than 100 feet?

27. f. When will the ball be at a height of 40 feet? 4.53 seconds

28. g. When will the ball hit the ground? g. When will the ball hit the ground? Put 0 in y2 and find the intersection! 4.98 seconds

29. Now try it on your own!