Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Opener-SAME SHEET-12/6Find each square root.

Solve each equation.

5. –6x = –60 6.

7. 2x – 40 = 0 8. 5x = 3

6

11

–25

1. 2.

3. 4.

x = 10 x = 80

x = 20

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots9-7 Solving Quadratic Equations

by Using Square Roots

Holt Algebra 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Find the zeros of each function.

2. f(x) = x2 – 9x + 20

1. f(x)= x2 –7x

3. x2 – 10x + 25 = 0

Find the roots of each equation using factoring.

5-3 Homework Quiz

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

5-3 Homework Quiz B

2. 2x2 + 7x – 15 = 0

1. -4x - 12 = -x2

Solve by factoring

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Solve quadratic equations by using square roots.

Objective

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Some quadratic equations cannot be easily solved by factoring. Square roots can be used to solve some of these quadratic equations. Recall from lesson 1-5 that every positive real number has two square roots, one positive and one negative.

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Negative Square root of 9

When you take the square root of a positive number and the sign of the square root is not indicated, you must find both the positive and negative square root. This is indicated by ±√

Positive and negativeSquare roots of 9

Positive Square root of 9

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

The expression ±3 is read “plus or minus three”

Reading Math

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Example 1A: Using Square Roots to Solve x2 = a

Solve using square roots. Check your answer.

x2 = 169 x2 = –49 x2 = 121 x2 = 0

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

If a quadratic equation is not written in the form x2 = a, use inverse operations to isolate x2 before taking the square root of both sides.

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Example 2A: Using Square Roots to Solve Quadratic Equations

1. x2 – 10 =26 2. 8x2 = 32

3. 25x2 – 1 = 0 4. x2 – 32 = 17

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Check It Out! Example 2a

Solve by using square roots. Check your answer.

100x2 + 49 = 0

There is no real solution.

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

When solving quadratic equations by using square roots, you may need to find the square root of a number that is not a perfect square. In this case, the answer is an irrational number. You can approximate the solutions.

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Example 3A: Approximating Solutions

Solve. Round to the nearest hundredth.

x2 = 15

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Example 4: Application

Ms. Pirzada is building a retaining wall along one of the long sides of her rectangular garden. The garden is twice as long as it is wide. It also has an area of 578 square feet. What will be the length of the retaining wall? Let x represent the width of the garden.

Holt Algebra 1

9-7 Solving Quadratic Equations by Using Square Roots

Lesson Quiz: Part 1

Solve using square roots. Check your answers.

1. x2 – 195 = 1

2. 4x2 – 18 = –9

3. 2x2 – 10 = –12

4. Solve 0 = –5x2 + 225. Round to the nearest hundredth.

± 14

± 6.71

no real solutions