Unit 2-A Day 3. Quadratic Regressions
Example 1. A pumpkin tossing contest is held each year. One catapult launches pumpkins from 25 feet
above the ground at a speed of 125 ft/sec. The table below shows the horizontal distance the pumpkin
travels when launched at different angles. Find the best-fitting quadratic model.
Angle (degrees)
20
30
40
50
60
70
Distance (feet)
372
462
509
501
437
323
Start by doing Stat Plots like yesterday (enter data, do a stat plot, graph it--should look like parabola)
To Perform a Quadratic Regression (which calculates then draws the “Best-Fit” curve for your data):
Hit STAT then > (right arrow) to CALC then 5 (to do a Quadratic Regression) then 2nd 1 (for L1) then
comma, then 2nd 2 (for L2) then comma, then VARS then > (right arrow) then ENTER, ENTER, ENTER.
On your screen should be the words QuadReg followed by an equation and values for a, b, and c. These
make the values that fit the quadratic equation y = ax2 + bx + c.
Now hit GRAPH and you will see not only your stat plot, but also the “Best-Fit” curve for the data. If you
hit the y= key, you will see the equation written in y1.
a= -.26
b= 22.59
c=23.03
y = -.26x2 + 22.59x + 23.03
Question 1. Find the distance the pumpkin travels if the angle is 75 degrees. A: 246.85 ft.
* Do like yesterday 2nd calc value 75 enter (make sure window large enough)
Question 2. Find the maximum distance the pumpkin travels. At what angle does this occur?
* To find this, hit TRACE. Notice where your cursor is (it’s on the stat plot.) You must downarrow to get on curve. Now 2nd calc 4 then left arrow enter, two right enter, one left enter.
A. Maximum distance travelled is 511.09 feet. This occurs at an angle of 43.21 degrees.
TTCM Unit 2-A Day 3: Quadratic Regressions Homework.
p. 57- 60: 9, 10, 12, 13, 16, 21, 26. (a) Perform the quadratic regression
(b) List a, b, c and the equation y = ax2 + bx + c
(c) Answer the corresponding question listed below
#9. Find predicted income in 2014.
#10. Find the maximum height the ball reaches
#12. Find the maximum height the airline reaches.
#13. Find % farmed in 2014.
#16. What year was there the maximum number of hospitals?
#21. How much at 30 degrees?
#26. What selling price for the calculators will give the maximum profit?
TTCM Unit 2-A Day 3: Quadratic Regressions Homework.
p. 57- 60: 9, 10, 12, 13, 16, 21, 26. (a) Perform the quadratic regression
(b) List a, b, c and the equation y = ax2 + bx + c
(c) Answer the corresponding question listed below
#9. Find predicted income in 2014.
#10. Find the maximum height the ball reaches
#12. Find the maximum height the airline reaches.
#13. Find % farmed in 2014.
#16. What year was there the maximum number of hospitals?
#21. How much at 30 degrees?
#26. What selling price for the calculators will give the maximum profit?
TTCM Unit 2-A Day 3: Quadratic Regressions Homework.
p. 57- 60: 9, 10, 12, 13, 16, 21, 26. (a) Perform the quadratic regression
(b) List a, b, c and the equation y = ax2 + bx + c
(c) Answer the corresponding question listed below
#9. Find predicted income in 2014.
#10. Find the maximum height the ball reaches
#12. Find the maximum height the airline reaches.
#13. Find % farmed in 2014.
#16. What year was there the maximum number of hospitals?
#21. How much at 30 degrees?
#26. What selling price for the calculators will give the maximum profit?