# Final Project

by

### Helene Chidsey and Lou Ann Lovin

Family of Hyperbolas

Considerations of the graphs of the equation,
#### xy = ax + by + c.

For an eploration of this equation click
here.

GSP Scripts and Sketches

Construction of a rhombus, parallelogram, isosceles trapezoid, and an isosceles
triangle given particular elements. GSP
Page.

The Lidless Box Problem

Given a rectangular sheet of cardboard 15 in. by 25 in., what size square
should be cut from each corner to produce a box with a volume of 400 cu.
in.? What size square would produce the maximum volume? (The square cut
from each corner needs to be the same size since we want to fold each side
up along the cuts to form a lidless box.) Below are three ways to investigate
this problem.

**Click here to look at
an Excel (Spreadsheet) investigation.**

**Click here
to look at an Algebra Xpresser (Relational Grapher) investigation.**

**Click here to look at a Geometer's SketchPad (Interactive
Geometric Environment) investigation.**

This investigation is interactive. The user can see the dimensions and volume
of the box change either by using the provided animation or by manually
manipulating the box.

## Ratio of Areas

Consider any triangle ABC and a point p inside the triangle. Draw lines
AP, BP, and CP extended to their intersections with the opposite sides in
points D,E, and F respectively. Various explorations based on this triangle
can be viewed by clicking here.

## An Exploration of Linear Functions

Combinations of operations (addition, multiplication, division, and composition)
on various linear functions. Click
here to view the investigation.

**Return to
Helene's Webpage**