Section 7.7
Finding Quadratic Models
Finding a Quadratic Model in Standard Form
Finding an Equation of a Quadratic Model
Example
The numbers of house calls
paid by Medicare are shown
in the table for various years.
Let f (t) be the number of
house calls (in millions) paid
by Medicare in the year that
is t years since 1995. Find an
equation of a model to
describe the situation.
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 2
Finding a Quadratic Model in Standard Form
Finding an Equation of a Quadratic Model
Process
Solution
Continued
4. Create a scatter-gram and use the regression
feature of the calculator to find the appropriate
model that fits the data.
Calculator
• Using the graphing calculator’s quadratic
regression feature:
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 3
Determining Which Type of Model to Use
Determining Which Model to Use
Example
The number of federal
documents that are
classified has been
increasing; so has the cost
of keeping these documents
secret (see the table).
Let c be the federal cost of secrecy (in billions of
dollars) in the year that is t years since 1990. Find
the equation of a model to describe the situation
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 4
Determining Which Type of Model to Use
Determining Which Model to Use
Example
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 5
Determining Which Type of Model to Use
Determining Which Model to Use
Solution
• Use a graphing calculator to graph
a scattergram
• Use a graphing calculator find an
exponential regression model and a
quadratic regression model
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 6
Determining Which Type of Model to Use
Determining Which Model to Use
Solution
Exponential Model
Section 7.7
Quadratic Model
Lehmann, Intermediate Algebra, 4ed
Slide 7
Determining Which Type of Model to Use
Selecting a Model
Process
When performing step 1 of the modeling process, we
must decide whether a linear function, an exponential
function, a quadratic function, or none of these is
suitable for modeling the situation. Here are the
criteria for selecting a model:
• The graph of the model should fit the points well.
• The model should make sense within the context of
the authentic situation.
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 8
Determining Which Type of Model to Use
Four-Step Process
Process
To find a model and make estimates and predictions,
1. Create a scattergram of the data. Decide whether a
line, an exponential curve, a parabola, or none of
these comes close to the points.
2. Find an equation of your model.
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 9
Determining Which Type of Model to Use
Four-Step Process
Process Continued
3. Verify that your equation has a graph that comes
close to the points in the scattergram. If it doesn’t,
check for calculation errors or use different points
to find the equation. An alternative is to
reconsider your choice of model in step 1.
4. Use your equation of the model to draw
conclusions, make estimates, and/or make
predictions.
Section 7.7
Lehmann, Intermediate Algebra, 4ed
Slide 10