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. _______________________.

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?

Homework Answers

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.

Review 2:

List the intervals where theGraph is increasing.

List the intervals where theGraph is decreasing.

What is the limit as “x” Approaches infinity?

What is the limit as “x”Approaches -infinity?

You Do

16

(1, 18) List the intervals where theGraph is increasing.

List the intervals where theGraph is decreasing.

What is the limit as “x” Approaches infinity?

What is the limit as “x”Approaches -infinity?

Standard Form Vertex Form

What is the vertex form of y = 2x2 + 10x + 7 ?

You may either complete the square or use your calculator.

You Do

Write the function in vertex form.

y = x2 – 4x + 6

Quick Check1. In your own words, define vertex, zeroesand

axis of symmetry of a parabola.

2. Find the vertex and zeros of y = 3x2 – 4x – 2

Quadratic Regression

What is the difference between a quadratic function and a quadratic regression?

QuadReg 1. STAT: edit. 2. Enter the values of the _____________ variable in L1. 3. Enter the values of the _____________ variable in L2. 4. Make sure your calculator is set to_______________ so that

you can observe the ______________ _____________, and determine how good a fit your model is.

5. 2nd: Y= 6. Turn on the first STAT Plot 7. STAT CALC 8. QuadReg (number ____).

R2

Instead of an r value, quadratic regressions have an r2.R2tells us :

What percentage of the time the model will be a good fit for the data.

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 r2 value? How good a model is this?

US Cigarette consumption

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?

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)

The Chesapeake Bay

Average Monthly Temperatures of the Chesapeake Bay

Month

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Temp 31 34 44 54 64 72 76 75 68 57 47 36

a. What is the independent variable? b. What is the dependent variable? c. Enter your data in L1 and L2. 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=______

Cont…

e. What is the quadratic regression equation?

f. What is r2? 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?

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

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.Time 0.2 0.6 1 1.2 1.5 2 2.5 2.8 3.4 3.8 4.5Ht. 92 110 130 134 142 144 140 132 112 90 44

a. Show a scatter plot of the data. What is the independent variable, and what is the dependent variable?

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

c. When will the ball be at a height of 150 feet?

d. When will the ball be at a height of 100 feet?

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

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

g. When will the ball hit the ground?

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

b. What prediction equation (mathematical model) describes

this data?

QUADRATIC!!

c. When will the ball be at a height of 150 feet?

Height (y)Put 150 in y2.

What happened?!? Explain.

d. When will the ball be at a height of 100 feet?

Put 100 in y2 and find the intersection!

.34 seconds and

3.65 seconds

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

65334 .x.

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

4.53 seconds

g. When will the ball hit the ground?

Put 0 in y2 and find the intersection!

4.98 seconds

Now try it on your own!