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
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
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: Quadratic Equations II - Complete the Square

Overview

This lesson covers the third of four methods for algebraically solving a quadratic equation (the first two being factoring and the root method). The complete the square method has some pretty cool history in that it was used in antiquity to solve quadratic equations purely geometrically even before algebra was invented.

Objectives

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

• 11.3.1 Recognize quadratic equations that can be solved by the complete the square method
• 11.3.2 Find the number that must be added to an expression of the form x2+bx to make it a perfect square trinomial so that it can be written as a binomial squared
• 11.3.3 Solve quadratic equations algebraically by the complete the square method
• 11.3.4 Appreciate that the complete the square method has historical significance in mathematics particularly in terms of solving quadratic purely geometrically

Terminology

Define: perfect square trinomial, binomial squared, complete the square method of solving a quadratic equation

Supplementary Resources

Read either CTS at Math is Fun or Geometrical Approach to CTS by Shelley Walsh. (Unfortunately the Shelley Walsh site is often "down" so I'm providing a copy of the article here but the links in it likely won't work.)