Modeling With Quadratic Functions Worksheet - Section 2.4
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82.4
Modeling with Quadratic Functions
Essential Question
Essential Question
How can you use a quadratic function to model
C
a real-life situation?
OMMON
C
ORE
Modeling with a Quadratic Function
Learning Standards
HSA-CED.A.2
Work with a partner. The graph shows a
HSF-IF.B.6
P
HSF-BF.A.1a
quadratic function of the form
HSS-ID.B.6a
P(t) = at
+ bt + c
2
P(t) = at
2
+ bt + c
which approximates the yearly profi ts for a
company, where P(t) is the profi t in year t.
a. Is the value of a positive, negative,
or zero? Explain.
b. Write an expression in terms of a and b that
represents the year t when the company
t
Year
made the least profi t.
c. The company made the same yearly profi ts in 2004 and 2012. Estimate the year in
which the company made the least profi t.
d. Assume that the model is still valid today. Are the yearly profi ts currently
increasing, decreasing, or constant? Explain.
Modeling with a Graphing Calculator
Work with a partner. The table shows the heights h (in feet) of a wrench t seconds
after it has been dropped from a building under construction.
Time, t
0
1
2
3
4
Height, h
400
384
336
256
144
a. Use a graphing calculator to create a scatter
400
plot of the data, as shown at the right. Explain
why the data appear to fi t a quadratic model.
MODELING WITH
MATHEMATICS
b. Use the quadratic regression feature to fi nd
a quadratic model for the data.
To be profi cient in math,
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5
you need to routinely
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c. Graph the quadratic function on the same screen
interpret your results in
as the scatter plot to verify that it fi ts the data.
the context of the
situation.
d. When does the wrench hit the ground? Explain.
Communicate Your Answer
Communicate Your Answer
3.
How can you use a quadratic function to model a real-life situation?
4.
Use the Internet or some other reference to fi nd examples of real-life situations
that can be modeled by quadratic functions.
Section 2.4
Modeling with Quadratic Functions
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