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Unit 10B – Quadratics - Chapter 9 Name:

The calendar and all assignments are subject to change. Students will be notified of any changes

during class, so it is their responsibility to pay attention and make any necessary changes.

All assignments are due the following class period unless indicated otherwise.

Monday Tuesday Wednesday Thursday Friday

4

MapTesting

5

Section 9.1

Prop of Radicals

6

Section 9. 1b

Properties of

Radicals

7

Section 9.3

8

Quick Quiz

Section 9.4 Completing

the Square

11

Section 9.4b

12

Section9.4c/ 9.5a

Quadratic Formula

13

Section 9.5 b

14

9.5c

15

Review Quadratics

18

Review Quadratics

19

Test on Solving

Quadratics

Section Page Assignment

9.1 p. 485

9.1b p. 486

9.3 p. 501

9.4 p. 511

9.4b

9.5a p. 521

9.5b

Chapter 9 Review

2

Lesson 9.1 – Properties of Radicals Algebra 1

Essential Question How can you multiply and divide square roots?

For each operation with square roots, compare the results obtained using the two indicated orders of

operations. What can you conclude?

a. Square Roots and Multiplication

Is 4 9 equal to 4 9?

In general, is a b equal to ?a b Explain your reasoning.

b. Square Roots and Division

Is 100

4 equal to

100

4

In general, is a

b equal to ?

a

b Explain your reasoning.

Core Concepts

Product Property of Square Roots

Words The square root of a product equals the product of the square roots of the

factors.

Numbers 9 • 5 9 • 5 3 5

Algebra • , where , 0ab a b a b

1. Simplifying Radicals with the Product Property

Simplify each radical into its simplest form.

(a) (b) (c) (d) (e)

(f) (g)

50 125 48 300 72

128 288

1 EXPLORATION: Operations with Square Roots

3

Quotient Property of Square Roots

Words The square root of a quotient equals the quotient of the square roots of the

numerator and denominator.

Numbers 3 3 3

4 24 Algebra , where 0 and 0

a a a b

b b

2. Simplifying Radicals with the Quotient Property

Simplify each radical into its simplest form.

(a) (b) (c) (d) (e)

3. Simplify each radical into its simplest form.

(a)

6162g (b) 7512h (c) 4

196

r (d)

3

2

49

64

x

y

Lesson 9.1 – Properties of Radicals – Day 2 Algebra 1

A radical is simplest form when 3 conditions are met:

No radicands have…

No radicands contain…

No radicals appear in the…

9

25

25

18

6

72

90

40

50

32

4

1. Dividing Radicals (Rationalizing the Denominator) Simplify the Radical

(a) (b) (c)

(d) (e) ba

b

(f) 22

42

Practice Dividing Radicals

2. 7

4 3.

5

5 4.

2

10 5.

48

3

6. 75

9

7.

210

6

8.

37

12

2

5

14

7

35

6

23

4

5

Lesson 9.1 Worksheet Name _____________________________

I. Simplify each expression completely.

1. √ 2. √ 3. √

4. √ 5. √ √ 6.

√

7. √

8. √

9. 7√

10. √

11. √

12.

√

13. √

√ 14. √

15.

√

√

6

Lesson 9.3 – Solving Quadratic Equations Using Square Roots Algebra 1

Essential Question How can you determine the number of solutions of a quadratic equation of the form ax2 + c = 0?

1. Finding Square Roots Evaluate.

(a) (b) (c) (d)

2. What is the square root of 36?

3. Solving Quadratics Equations in the Form:

Solve the following quadratic equations.

(a) (b) (c)

4. Solving Quadratics Equations in the Form:

Solve the following quadratic equations.

(a) (b) (c)

(d) ( e) 2

2 196x (f) 2

2 7 49x

81 100 64 9

cx 2

812 x 172 x 52 x

02 cax

01222 x 012 x 0273 2 x

06012 2 x

7

5. Application Exercise – Falling Object Model

You have entered Mr. Esbrook’s first annual “egg dropping

contest”. The goal is to create a container for an egg so it can be

dropped from a height of 32 feet without breaking the egg. In you

quest to become egg-dropping champion, you have asked your

Algebra class to determine the time it will take for the egg

container to hit the ground. About how long will it take for the

egg’s container to hit the ground? Assume there is no air

Algebra: Section 9.1/ 9.3 Worksheet

Name______________________________________________Date____________________Hour______

Solve each equation using square roots. Simplify square roots if necessary. There should be no decimal answers.

1. x2 = 100 2. 2y2 = 32 3. ¼ a2 = -6

4. 10 – 2x2= 4 5. 7y2 + 14 = 0 6. 3b2 – 6 = 9

7. ½ x2 – 7 = 1 8. 2x2 + 5 = 9 9. -4x2 + 6 = -394

10. 6 – 3x2 = 27 11. 2

81 3 1 49x 12. 2

16 3 25x

8

simplify.

√ 13. √ 14. √

15. √

16. √

17. -3√

18. -5 √

√ 19. Find the area of a square with side length √

20. Find the area of a triangle with height √ and base √ .

21. Using the Falling Object Model found in section 9.1. Determine approximately how long it will take a I-

phone to hit the ground when dropped from a window 25 feet above the ground.

Lesson 9.4(a) – Completing the Square (w/ Leading Coefficient 1) Algebra 1

1. Completing the Square Complete the square so that each expression is a perfect square trinomial. Then factor the trinomial.

(a) (b) (c)

xx 122 xx 82 xx 302

Completing the Square To complete the square for any quadratic

expression in the form

add ____________ of the second coefficient (b)

_____________ to the end.

9

2. Solving Quadratic Equations by Completing the Square Solve each quadratic equation by completing the square.

(a) (b)

(c) (d)

Lesson 12.4(b) – Completing the Square (w/ Leading Coefficient 1) Algebra 1

Warm-Up Exercise Solve by Completing the Square.

(a) (b) Solving Quadratic Equations by Completing the Square Solve each quadratic equation by completing the square.

1. 2.

24102 xx 07262 xx

0422 xx 03 2

12 xx

01422 xx 7142 xx

41082 2 xx 0848 2 xx

10

3. 4. 210 13 9 0x x

5. 23 6 1 0x x 6.

212 8 2 0x x

In Exercises 7-12, determine whether the quadratic function has a maximum or minimum value.

Then find the value.

7. 2 4 3y x x 8. 2 6 10y x x 9. 2 8 2y x x

10. 2 10 8y x x 11. 23 3 1y x x 12. 24 8 12y x x

0263 2 xx

11

13. Choosing a Method to Solve a Quadratic Determine the easiest method to solve the quadratics below. Tell which method you used, and then solve the equation.

(a) (b)

(c)

Lesson 9.5(a) –The Quadratic Formula Algebra 1

Essential Question How can you derive a formula that can be used to write the solutions of any quadratic equation in standard form?

The following steps show a method of solving 2 0.ax bx c