Math 30-2
Polynomial Functions: Lesson #5
Modeling Data With a Curve of Best Fit
(Quadratic & Cubic Regression)
Objective: By the end of this lesson, you should be able to:
- graph quadratic or cubic data and use technology to find a regression equations that fits
the data
- interpret the graph of a polynomial function that models a real-life situation
Sometimes data does not follow a linear pattern, but may be best modeled by a ______________
or ____________ polynomial function. This is called a __________ of best fit.
To find a quadratic or cubic regression on your calculator, but instead of choosing 4:LinReg,
choose:
 5:QuadReg for quadratic regression
 6:Cubic Reg for cubic regression
e.g. 1) The following table shows the average retail price of a litre of gas for a selection of years
in a 30-year period beginning in 1979.
Years after
Price of gas
Years after
Price of gas
1979
(¢/L)
1979
(¢/L)
0
21.98
17
58.52
1
26.18
20
59.43
2
35.63
22
70.56
3
43.26
23
70.00
4
45.92
24
74.48
7
47.78
25
82.32
8
47.95
26
92.82
9
47.53
27
97.86
12
57.05
28
102.27
14
54.18
29
115.29
a) Use technology to graph the data as a scatter plot. What type of polynomial function
would be best to model the data? Explain.
b) Determine the appropriate regression equation that models the data. Round
coefficients to four decimal places.
c) Use the regression equation to estimate the price of gas the year you were born.
Math 30-2
Polynomial Functions: Lesson #5
d) Estimate the year in which the price of gas reached $1.00/L.
e.g. 2) Josie hit a golf ball from the top of a hill. The height of the ball above the green each
second is given in the table below.
1
2
3
4
5
Time (s)
52.5
73.2
74.6
55.8
16.1
Height (m)
a) Use technology to graph the data as a scatter plot. What type of polynomial function
would be best to model the data? Explain.
b) Determine the equation of the regression equation that best models the data.
c) What is the maximum height the golf ball reached to the nearest hundredth?
d) What is the y-intercept? What does it represent in this situation?
e) When did the ball hit the ground, to the nearest hundredth?
Assignment:
Quadratic & Cubic Regression Assignment