# Chapter 11: Algebra and Geometry Connections

## Introduction

As you’ve seen, to solve quadratic equations you often have to take the square root of a number. As you might expect then, when graphed, square root functions form half of a parabola. In this chapter you’ll graph such functions. Square roots are a type of radical, which is the second focus of this chapter. You’ll also perform operations such as addition, subtraction, multiplication, and rationalizing the denominator on a variety of radical expressions and equations to simplify and solve them. You’ll then apply the knowledge of square roots and radicals you’ve gained to solve right triangle problems, to find the distance between two points, and to find the midpoint of a line segment.

## Chapter Outline

- 11.1. Graphs of Square Root Functions
- 11.2. Shifts of Square Root Functions
- 11.3. Raising a Product or Quotient to a Power
- 11.4. Simplification of Radical Expressions
- 11.5. Applications Using Radicals
- 11.6. Radical Equations
- 11.7. Equations with Radicals on Both Sides
- 11.8. Pythagorean Theorem and its Converse
- 11.9. Solving Equations Using the Pythagorean Theorem
- 11.10. Applications Using the Pythagorean Theorem
- 11.11. Distance Formula
- 11.12. Midpoint Formula

### Chapter Summary

## Summary

This chapter begins by focusing on the graphs of one type of radical called square root functions. It teaches how to graph simple square root functions and addresses what types of mathematical operations performed on those functions produce vertical and horizontal shifts in their graphs. It then moves on to a more general discussion of radicals, introducing properties and special cases that can be used to solve radical equations. An important geometric application of radicals, the Pythagorean Theorem, is covered next as a way to find the unknown values of a right triangle. The chapter closes with two more geometric applications: the Distance Formula and the Midpoint Formula.