Finding Quadratic Models

Section 7.7

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 2

Finding a Quadratic Model in Standard FormFinding an Equation of a Quadratic Model

ExampleThe 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.

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 3

Finding a Quadratic Model in Standard FormFinding an Equation of a Quadratic Model

Solution4. Create a scatter-gram and use the regression

feature of the calculator to find the appropriate model that fits the data.

• Using the graphing calculator’s quadratic regression feature:

Process Continued

Calculator

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 4

Determining Which Type of Model to UseDetermining Which Model to Use

ExampleThe 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

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 5

Determining Which Type of Model to UseDetermining Which Model to Use

Example

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 6

Determining Which Type of Model to UseDetermining 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

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 7

Determining Which Type of Model to UseDetermining Which Model to Use

Solution Exponential Model Quadratic

Model

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 8

Determining Which Type of Model to UseSelecting a Model

ProcessWhen 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.

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 9

Determining Which Type of Model to UseFour-Step Process

ProcessTo 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.

Lehmann, Intermediate Algebra, 4edSection 7.7 Slide 10

Determining Which Type of Model to UseFour-Step Process

Process Continued3. 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.