Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis

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:

• 11.5.1 Understand that quadratic functions can be used to model a variety of real-life applications
• 11.5.2 Solve geometry application problems involving area and/or perimeter using a quadratic equation
• 11.5.3 Solve geometry application problems involving right triangles and the Pythagorean Theorem using a quadratic equation

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!