Chapter 9B

Table of Contents

o Day 1: SWBAT: Solve Quadratic Equations by Factoring and Graphically

Pgs: 1-6

HW: Pages 7 - 8

o Day 2: SWBAT: Solve Quadratic Word Problems by Factoring

Pgs: 9-15

HW: Pages 16-19

o Day 3: SWBAT: Solve Consecutive Integer Word Problems by Factoring Quadratic Equations

Pgs: 20-24

HW: Pages 25-26

o Day 4: SWBAT: Solve Quadratic – Linear Systems Algebraically

Pgs: 27-30

HW: Pages 31-32

o Day 5: SWBAT: Write a quadratic equation that has given roots using reverse factoring

Pgs: 33-37

HW: Page 38

o Day 6: SWBAT: Review Solving Equations Quadratics by using a variety of problems

Pgs: 39-48

HW: Finish this Section

1

Day 1

Warm - Up: Factor Each.

1. 2. x2 - 4x - 12

3. x2 - 64 4. x2 - 6x

You will Learn how to Solve Quadratic Equations two ways:

Method 1: Solve by Graphing

Method 2: Solve by Factoring (Preferred Method)

2

x2 + 8x + 15 = 0

Solution: x = _____ or x = _____

Solution: x = _____ or x = _____

3

Example 3: Use the Zero Product Property

Use the Zero Product Property to solve each equation.

A. (x – 3)(x + 7) = 0 B. x(x - 5) = 0

Example 2: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring.

C. x2 – 12x + 36 = 0 D. x

2 + 4x = 21

4

Practice: Solve the quadratic equation by factoring.

3. x2 = -3x + 10 4. x

2 + 2x = 8

Example 3: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring.

E. x2 – 5x = 0 F. x

2 = -2x

Practice: Solve the quadratic equation by factoring.

5. x2 + 7x = 0 6. x

2 = 11x

5

Example 4: Solving Quadratic Equations by Factoring

Solve the quadratic equation by factoring.

G. x2 – 16 = 0 H. 4x

2 = 25

Practice: Solve the quadratic equation by factoring.

7. x2 – 49 = 0 8. 9x

2 = 100

Challenge

The graph below represents a quadratic function of the form y x2 bx c . Use the graph

to determine the zeros of the function. Then, determine the binomial factors of the function, and

express the quadratic function in its y x2 bx c form.

6

SUMMARY

Exit Ticket

1.

2.

7

Day 1 – HW

Solve each by Factoring.

1. x2 + 11x + 24 = 0

2. x2 - 225 = 0 3. x

2 - 3x = 0

4. x2 + 3x = 28

5. x2 = 81 6. x

2 = 14x

7. x2 = 4x + 12

8. 25m2 = 36 9. x

2 = -10x

10. x2 - 14 = 5x

11. 3x2 = 48 12. 2a

3 = 12a

2

8

13. x2 - 4x + 4 = 0

Solution: _________________

14. 2x2 + 4x – 6 = 0

Solution: _________________

9

Day 2 – Word Problems and Quadratic Equations

SWBAT: Solve More Quadratic Equations by Factoring

Warm – Up

1.

Quadratic Equations and Proportions

10

Section 1: Solving Quadratic Equations involving Proportions

1)

2)

3)

4)

11

Solve each Proportion.

12

13

Section 2: Solving Quadratic Equations involving Word Problems

Example 9: Solve.

The square of a number increased by twice the number is 48. Find both solutions.

Practice: Solve.

1) When 10 is subtracted from the square of a number the result is three times the

number. What is the positive solution?

14

Example 10: Solve.

The shorter side of a rectangle is 3 less than the longer side. The area is 54. Find

the length and width.

Practice: Solve.

1) The length of a rectangle is four feet longer than the width. The area is 21. Find

the dimensions.

15

Challenge Problem: One leg of a right triangle is 1 cm longer than the other leg. The hypotenuse measures 5 cm.

Find the measure of each leg of the triangle.

Summary

Exit Ticket

1.

2.

16

Homework

Section 1: Solve each Proportion.

1)

2)

3)

17

4)

5)

6)

7)

18

Section 2: Word Problems

8) The square of a number is equal to 24 more than twice the number. Find the

negative number.

9) The square of a number is decreased by three times the number is ten. Find

the positive number.

10) When two times a number is subtracted from the square of a number

the result is zero. Find both numbers

11) The square of a number is decreased by five times the number is 24.

Find the number.

19

Section 3: Area Word Problems

12) The shorter side of a rectangle is 24 less than the longer side. The area

is 81. Find the length and the width.

13) The length of a rectangle exceeds the width by 6. The area of the

rectangle

is 27. Find the length and the width.

14) The length of a rectangle is one more than the width. The area is 56.

Find the length and the width.

15) The length of a rectangle is eight more than the width. The area is 9.

Find the length and the width.

20

Day 3 – Consecutive Integer Word Problems and Quadratic Equations

SWBAT: Solve Consecutive Integer Word Problems by Factoring Quadratic Equations. Warm – Up:

Recall:

Consecutive Integers are integers that follow one another in order.

Ex: {5, 6, 7, 8}

{-5, -4, -3, -2}

Rule:

Consecutive Even/ODD Integers are even or odd integers that follow one another in

order.

Ex: {2, 4, 6, 8} Ex: {3, 5, 7, 9}

{-12, -10, -8, -6} {-5, -3, -1, 1}

Rule:

21

Example 1: The product of two consecutive positive odd integers is 1 less than four times their sum. Find the two positive integers.

Example 6: Solve.

Find three consecutive integers such that the square of the first is equal to one more

than twice the second.

Example 2: The product of two consecutive integers is 56. Find the integers

Answer: 7 and 9

22

Practice: Solve.

The product of two consecutive even integers is 48. Find the integers

Example 3: The product of two consecutive integers is three less than three times their sum. Find the integers.

Practice: Solve.

The product of two consecutive odd integers is 1 less than twice their sum. Find the integers.

23

Example 4: The product of two consecutive integers is 5 more than three times the larger. Find the integers.

Example 5:

Find three consecutive odd integers such that the product of the first and third is

one more than four times the second.

Practice: Solve.

Find three consecutive integers such that the product of the first and second is 2

more than three times the third.

24

Challenge

SUMMARY

Exit Ticket

25

Day 3 Consecutive Integer Homework

1) The product of two consecutive integers is 120. Find the integers

2) Find two consecutive even integers such that the square of the smaller is 10 more than the larger.

3) The product of two consecutive integers is six less than their sum. Find the integers.

4)

26

5) Find three consecutive even integers such that the product of the first and

third is equal to three times the second.

6) Find three consecutive odd integers such that the square of the first

increased by twice the second is equal to two less than three times the third.

7) Find three consecutive even integers such that the product of the first and

the second is 8 more than 38 times the third.

27

Day 4

SWBAT: Solve a Quadratic - Linear System Algebraically

Warm – Up

28

Exercise 2: Solve the Quadratic Linear System below. Check your answer

y = x2 – x - 6 y = 2x - 2

Step 1: Use Substitution to replace the expressions for “each y” equal to each other.

Make sure that both equations are solved for “y” first!

__________________ = ____________

Step 2: Solve the Quadratic so that we have an equation in the form of ax2 + bx + c = 0

Step 3: Factor

Step 4: Set each factor equal to zero.

Step 5: Solve for y by plugging in the x-value into the linear equation.

x = ____ y =

Step 6: Write your answer(s) as a point.

Solutions =

x = ____ y =

29

30

CHALLENGE PROBLEM

SUMMARY

EXIT TICKET

31

HOMEWORK – Quadratic Linear Systems

1. Solve algebraically:

y = x2 - 4x + 1

y = 2x - 4

The point(s) of intersection are: ____________________

______________________________________________________________________________

2. Solve algebraically:

y = x2 - 2x + 1

y = -x + 3

The point(s) of intersection are: ____________________

32

3. Solve algebraically:

y + 3x = x2 - 10

y + 10 = -5x

The point(s) of intersection are: ____________________

______________________________________________________________________________

4. Solve algebraically:

y = -x2 + 6x - 5

y = 7 – 2x

The point(s) of intersection are: ____________________

33

Day 5

SWBAT: Write a quadratic equation that has given roots using reverse factoring

Warm – Up

Up to this point we have found the solutions to quadratics by a factoring. Here we will take our solutions and work backwards to find what quadratic goes with the solutions. We will start with rational solutions. If we have rational solutions we can use factoring in reverse, we will set each solution equal to x and then make the equation equal to zero by adding or subtracting. Once we have done this our expressions will become the factors of the quadratic.

34

Example #2:

If the roots of a quadratic equation are 2 and 5, write the quadratic equation in the form

ax² +bx + c = 0.

Method 1 Method 2

________________________________________________________________________________

Practice:

1. If the roots of a quadratic equation are -3 and 2, write the quadratic equation in the form of

ax² +bx + c = 0.

2. If the roots of a quadratic equation are -2 and 2, write the quadratic equation in the form of

ax² +bx + c = 0.

3. If the roots of a quadratic equation are 1 and -6, write the quadratic equation in the form of

ax² +bx + c = 0.

4. If the root of a quadratic equation is 6, write the quadratic equation in the form of

ax² +bx + c = 0.

Answer:

35

Example #3: Write the equation of the quadratic equations below in the form of

ax² +bx + c = 0.

36

Practice: Write the equation of the quadratic equations below in the form of

ax² +bx + c = 0.

5.

6.

7.

37

Challenge

SUMMARY

Exit Ticket

1) Which factored form of a quadratic has roots of 4 and -3?

2)

38

Day 5 - Homework

Write a quadratic equation in the form of ax² +bx + c = 0 that has the given roots.

1. { -1 , -10 }

2. { 10 , -1 }

3. { 2 , -6 }

4. { 3 , -2 }

5. { -2 , -4 }

6. { 1 , -12 }

7. { -1 , -2 }

8. { 2 , -4 }

9. { 1 , -10 }

10. { -1 , -3 }

11. 5

12. { 6 , -1 }

13. { 4 , -1 }

14. { 2 , -5 }

15. { 4 , 1 }

16.

17. 18.

39

Chapter 9 Review – Quadratic Equations Review

SWBAT: Apply Their Knowledge on Solving Quadratic Equations

1. What are the solutions of (x + 4)(x – 2) = 0?

A) 4 and -2

B) -4 and -2

C) -4 and 2

D) 4 and 2

2. Solve x2 + 2x – 15 = 0 by factoring.

A) x = 5 and x = 3

B) x = 15 and x = 1

C) x = -5 and x = 3

D) x = -5 and x = -3

3. What are the solutions of: 0 = 2x2 – 50?

A) -4 and 4

B) -5 and 5

C) -2 and 2

D) -3 and 3

4.

40

5.

6. What is the solution set of the equation x2 – 3x = 0?

A) {0}

B) {0, 3}

C) {0, -3}

D) {3}

7. The solution set for the equation x2 + 4x = 5?

A) {-5, 4 }

B) {-4, 5}

C) {-5, 1}

D) {-1, 5}

41

8.

A) y = x2 + 7x - 10

B) y = x2 - 8x + 12

C) y = x2 - 7x + 10

D) y = x2 - 3x – 10

9.

10.

11.

42

12.

13.

14.

15.

43

16.

17.

18.

44

19.

20.

21.

45

22. Solve: x2 = 49.

23. Solve: 25x2 + 15 = 115

24. The square of a number is equal to three less than four times a number.

Find the numbers.

46

25. Solve algebraically.

3

142

xy

xxy

47

26. The length of a rectangle is four feet longer than the width. The area is 21.

Find the dimensions.

27. Find three consecutive odd integers such that the square of the first increased

by twice the second is equal to two less than three times the third.

48

28.

29.

29.