# Ch 1: Mathematical Modeling

### About This Chapter

## Mathematical Models - Chapter Summary and Learning Objectives

Mathematical models are used to explain the properties of various systems and figures. In the lessons in this chapter, our instructors will show you how to write and evaluate algebraic expressions for two-dimensional figures. Another lesson demonstrates the use of systems of linear equations to evaluate economic functions and profit functions. You will learn to find the minimum and maximum values of quadratic models, too. Instructors use examples from real life regarding cost determination and distance to show you how to write and evaluate linear models. By the end of this chapter, you should have a solid understanding of topics including:

- Writing equations that relate a two-dimensional figure's side lengths, perimeter and area
- Writing real-life linear models
- Applying linear equations to economic functions
- Determining minimum and maximum values of quadratic models

Video | Objective |
---|---|

Writing and Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures | Write and solve equations that relate a two-dimensional figure's side lengths, perimeter and area. |

Writing and Evaluating Real-Life Linear Models | Explore real-life models such as cost determination and d=rt. Utilize unit of measure conversion in some examples. |

Applying Systems of Linear Equations to Equilibrium Prices and Breakeven Point | Evaluate economic equilibrium and profit functions from linear models. |

Using Quadratic Models to Find Minimum and Maximum Values | Find minimum and maximum values of quadratic models. |

### 1. Writing & Evaluating Algebraic Expressions for Two-Dimensional Geometric Figures

Learning more about algebraic expressions and geometric figures will help you solve problems that occur in your life. In this lesson, you will use the perimeter of a two-dimensional geometric shape to solve a real-world problem.

### 2. Writing & Evaluating Real-Life Linear Models: Process & Examples

You make decisions about budgeting and other financial issues using linear models without even realizing it. Learn how to write and evaluate linear models.

### 3. Applying Systems of Linear Equations to Breakeven Point: Steps & Example

Businesses use breakeven points to determine price and sell products. Learn how to use systems of linear equations with revenue and cost functions to find the breakeven point.

### 4. Applying Systems of Linear Equations to Market Equilibrium: Steps & Example

Businesses use market equilibrium to determine price and sell products. Learn how to use systems of linear equations to find market equilibrium in this video lesson. Review what you know with a short quiz!

### 5. Using Quadratic Models to Find Minimum & Maximum Values: Definition, Steps & Example

Minimum and maximum values are found in parabolas that open up or down. In this lesson, learn how to find the minimum and maximum values algebraically and graphically.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the Math 105: Precalculus Algebra course

- Linear Equations & Inequalities
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105