polynomial folding box problem
Name_____________________________
Higher-degree polynomials are frequently used to model complicated data
sets.
For example, when plotting the distance versus time graph of a world-record
dragster quarter-mile run, the most accurate model to fit the data was a sixthdegree polynomial equation.
Higher-degree polynomials are used in many engineering formulas to calculate the changes
due to complex environmental phenomena over time. Higher-degree polynomials are
involved in equations for steel corrosion, variable resistors and the depth of river flow.
Bezier curves are a key element of the Adobe drawing model in Illustrator and
spline-based 3D modeling programs. Bezier curves are useful in graphic design
because they can be scaled indefinitely, allowing them to model smooth curves
of any shape. The Bezier curve is a parametric cubic, or third-order, equation.
Source: http://www.ehow.com/info_8050017_uses-higherdegree-polynomials.html
Objective:
The objective of this activity is to find a polynomial equation to model the volume of a box.
Then analyze the equation to find the dimensions that will produce a box with the maximum
volume.
Problem:
An 8.5” by 11” sheet of paper is folded into a box by
cutting equal-sized squares from each corner and
folding up the four edges.
http://www.mste.uiuc.edu/carvell/3dbox/
Procedure:
In your solution to the problem you must answer the
following questions. Be clear and neat in answering the questions.
1) Find a polynomial equation to model the volume of the box.
2) Make a sketch of the equation and label its roots.
3) Explain what the roots tell you in terms box volume and size of squares cut out.
4) What is the maximum volume? How much should you cut from the box?