An application of quadratic functions: Tree data

After this lesson, students should be able to

analyze data from the real world

apply this data to quadratic functions

make predictions

use Excel to graph quadratic functions for real-world data.

The data in the table below represents data from the lumber industry. The information listed approximates the number of board feet of lumber per tree in a forest for a given age.

 Age of Tree 100s of Board Feet 20 1 40 6 60 80 33 100 56 120 88 140 160 182 180 200 320

I. Plot the data in Excel.

II. Make conjectures.

III. Given any three points, write the equation of the graph.

IV. Test your equations using Excel.

I. Plotting the data in Excel

A. What is the shape of your graph?

B. What is the direction of opening? (up, down, left, right)

C. What is the width of your curve?

D. Is there a minimum point or a maximum point?

II. Making conjectures.

A. Based on Part I, describe the type of function that would predict the behavior of the graph.

B. Give your best prediction equation based on what you have learned in the last three sections.

III. Given any three points, write the equation of the graph.

A. What system of equations are you going to set up to find the equation? (refer to lesson on writing quadratic equations)

B. What is your final equation?

IV. Test your equations by using Excel.

A. First, graph your best prediction equation in Part II-B.

How close were you to the actual plotted data?

B. Second, graph the equation obtained in Part III.

How close were you to the actual plotted data?

C. Conclusions?