Holt Algebra 2

1-3 Square Roots

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Holt Algebra 2

1-3 Square Roots1-3 Square Roots

Holt Algebra 2

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Holt Algebra 2

1-3 Square Roots

2 Minutes to Ask Questions

Holt Algebra 2

1-3 Square Roots

Simplify, add, subtract, multiply, and divide square roots.

Objectives

Holt Algebra 2

1-3 Square Roots

radical symbol radicand principal rootrationalize the denominatorlike radical terms

Vocabulary

Holt Algebra 2

1-3 Square Roots

Use the graph of f(x) =x2 as a guide, describe the transformations and then graph each function.

Because h = –3, the graph is translated 3 units left. Because k = –2, the graph is translated 2 units down. Therefore, g is f translated 3 units left and 2 units down.

h k

g(x) = (x + 3)2 – 2

Identify h and k.

g(x) = (x – (–3)) 2 + (–2)

Quick Review From Friday…

Holt Algebra 2

1-3 Square Roots

Consider the function f(x) = 2x2 – 4x + 5.

Quick Review From Friday

a. Determine whether the graph opens upward or downward.

b. Find the axis of symmetry.

Because a is positive, the parabola opens upward.

The axis of symmetry is the line x = 1.

Substitute –4 for b and 2 for a.

The axis of symmetry is given by .

Holt Algebra 2

1-3 Square Roots

Consider the function f(x) = 2x2 – 4x + 5.

Example 2A: Graphing Quadratic Functions in Standard Form

c. Find the vertex.

The vertex lies on the axis of symmetry, so the x-coordinate is 1. The y-coordinate is the value of the function at this x-value, or f(1).

f(1) = 2(1)2 – 4(1) + 5 = 3

The vertex is (1, 3).

d. Find the y-intercept.

Because c = 5, the intercept is 5.

Holt Algebra 2

1-3 Square Roots

Square Roots…

Holt Algebra 2

1-3 Square Roots

List some perfect squares…

1, 4, 9, 16, 25, 36, etc…

What are the rest? Up to 300…(Write these down!)

Holt Algebra 2

1-3 Square Roots

Holt Algebra 2

1-3 Square Roots

Notice that these properties can be used to combine quantities under the radical symbol or separate them for the purpose of simplifying square-root expressions. A square-root expression is in simplest form when the radicand has no perfect-square factors (except 1) and there are no radicals in the denominator.

Holt Algebra 2

1-3 Square Roots

Find a perfect square factor of 32.

Simplify each expression. Example 2: Simplifying Square–Root Expressions

Product Property of Square Roots

Quotient Property of Square Roots

A.

B.

Holt Algebra 2

1-3 Square Roots

Product Property of Square Roots

Simplify each expression.

Example 2: Simplifying Square–Root Expressions

Quotient Property of Square Roots

C.

D.

Holt Algebra 2

1-3 Square Roots

Check It Out! Example 2

A.

Simplify each expression.

B.

Find a perfect square factor of 48.

Product Property of Square Roots

Quotient Property of Square Roots

Simplify.

Holt Algebra 2

1-3 Square Roots

Check It Out! Example 2

Simplify each expression.

C.

D.

Product Property of Square Roots

Quotient Property of Square Roots

Holt Algebra 2

1-3 Square Roots

If a fraction has a denominator that is a square root, you can simplify it by rationalizing the denominator. To do this, multiply both the numerator and denominator by a number that produces a perfect square under the radical sign in the denominator.

Holt Algebra 2

1-3 Square Roots

Simplify by rationalizing the denominator.

Example 3A: Rationalizing the Denominator

Multiply by a form of 1.

= 2

Holt Algebra 2

1-3 Square Roots

Simplify the expression.

Example 3B: Rationalizing the Denominator

Multiply by a form of 1.

Holt Algebra 2

1-3 Square Roots

Check It Out! Example 3a

Simplify by rationalizing the denominator.

Multiply by a form of 1.

Holt Algebra 2

1-3 Square Roots

Check It Out! Example 3b

Simplify by rationalizing the denominator.

Multiply by a form of 1.

Holt Algebra 2

1-3 Square Roots

Square roots that have the same radicand are called like radical terms.

To add or subtract square roots, first simplify each radical term and then combine like radical terms by adding or subtracting their coefficients.

Holt Algebra 2

1-3 Square Roots

Add.

Example 4A: Adding and Subtracting Square Roots

Holt Algebra 2

1-3 Square Roots

Subtract.

Example 4B: Adding and Subtracting Square Roots

Simplify radical terms.

Combine like radical terms.

Holt Algebra 2

1-3 Square Roots

Check It Out! Example 4a

Add or subtract.

Combine like radical terms.

Holt Algebra 2

1-3 Square Roots

Check It Out! Example 4b

Add or subtract.

Simplify radical terms.

Combine like radical terms.

Holt Algebra 2

1-3 Square Roots

Word Problem

• A stadium has a square poster of a football player hung from the outside wall. The poster has an area of 12,544 ft2. What is the width of the poster?

• 112 feet wide

Holt Algebra 2

1-3 Square Roots

Lesson Quiz: Part I

1. Estimate to the nearest tenth. 6.7

Simplify each expression.

2.

3.

4.

5.

Holt Algebra 2

1-3 Square Roots

Lesson Quiz: Part II

Simplify by rationalizing each denominator.

6.

7.

8.

9.

Add or subtract.

Holt Algebra 2

1-3 Square Roots

Wall Activity

Holt Algebra 2

1-3 Square RootsAssignment:

• Complete Worksheet

• (finish any worksheets not completed from last week.)

• Update notes/flipbook

• Ask any questions you still have