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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources

Course: Algebra III / Intermediate Algebra
Topic: Nonlinear Equations and Applications
Subtopic: Applications - Geometry & Pythagorean Theorem

Overview

Quadratic functions can be used to model a variety of real-life applications including geometry problems involving area and right-triangle problems involving the Pythagorean Theorem. Once the problem is translated into a quadratic equation, the methods we are studying for solving quadratics are used to find the solutions.

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Define: perimeter, area, Pythagorean Theorem

Text Notes

This section of your text likely covers several geometry-related applications. Focus on the Pythagorean Theorem problems. You may SKIP any "distance formula" and "midpoint formula" problems (whcih are covered in a precalculus course).

Supplementary Resources

Information on Pythagoras and the Pythagorean Theorem:
  Biography of Pythagoras of Samos
  Proof of the Pythagorean Theorem
  History of the Pythagorean Theorem

The Pythagorean theorem can be seen in terms of areas. The area of the yellow square (below) is a2, the area of the blue is b2, and these two areas together equal the green area, c2, thus a2+b2=c2. This holds no matter how big the red triangle is as long as it is a right triangle. Neat!

Watch: YouTube video: Pythagorean Theorem Water Demo