unit 4 solving quadratic equations homework 9 answer key

Quadratic Equation Worksheets (pdfs)

Free worksheets with answer keys.

Enjoy these free sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

• Solve Quadratic Equations by Factoring
• Solve Quadratic Equations by Completing the Square
• Quadratic Formula Worksheet (real solutions)
• Quadratic Formula Worksheet (complex solutions)
• Quadratic Formula Worksheet (both real and complex solutions)
• Discriminant Worksheet
• Sum and Product of Roots
• Radical Equations Worksheet

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

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Unit 4: Solving Quadratic Equations

Why are we studying this.

In this unit of study, students will continue to deepen their knowledge and understand of quadratic functions. Students will learn how to solve quadratic equations algebraically and interpret them in terms of the graph and in context.

Unit Schedule and Assignments

Weekly online, notebook: unit 4, table of contents & pages, hw #8: due 11/30, hw #10: due 12/14, hw #9: due 12/7, hw #11: due 12/21.

Daily Homework Assignments (w/Answer Keys)

Graphing: practice page.

Factoring Quadratic Expressions: Practice Page

8.1: #3-19 ODD

8.2: #1-15 odd, 9.1: #4-15 all + 18, 19, 22, 9.2: #1-15 odd + 23, 24, 9.3: #1-13 odd + 15-20 all, unit assessments, unit quizzes.

Mid-Unit Quiz #1: Solving Quadratics by Graphing and Factoring - Tuesday, December 4th (Per. 1 & 3) and Wednesday, December 5th (Per. 2)

Mid-Unit Quiz #2: Solving Quadratics by Square Roots, Completing the Square, and Quadratic Formula (POP QUIZ)

Unit 4 Assessment: Tuesday, December 18th (Per. 1 & 3) and Wednesday, December 19th (Per. 2)

Solving Quadratic Equations by Graphing

Unit Foldable: Solving Quadratic Equations

In Class Slides

Practice Page

Factoring Quadratic Expressions

In Class Slides (Day 1)

Factoring Trinomials Match Up

Factoring Quadratic Expressions (Orduna - video)

8.1-8.2: Solving Quadratic Equations by Factoring

8.1 Textbook Pages

8.2 Textbook Pages

In Class Slides (Day 2)

Notes/Practice Page

Solving Quadratic Equations by Factoring (Orduna - video)

For extra tutorial videos, visit my.hrw.com and check out...

8.1: Math on the Spot Video

8.2: Math on the Spot Video

9.1: Solving Quadratic Equations by Square Roots

9.1 Textbook Pages

Notes/Practice Pages

Choose Your Own Adventure

9.2: Solving Quadratic Equations by Completing the Square

9.2 Textbook Pages

Coloring Page

9.3: Solving Quadratics by Quadratic Formula

9.3 Textbook Pages

Quadratic Formula Tic-Tac-Toe

UNIT REVIEW RESOURCES

Word Problem Practice

Solving by Different Methods

Quadratics Puzzle

4 to 1 Review Game

x = 4 3 , x = −4 3 x = 4 3 , x = −4 3

y = 3 3 , y = −3 3 y = 3 3 , y = −3 3

x = 7 , x = −7 x = 7 , x = −7

m = 4 , m = −4 m = 4 , m = −4

c = 2 3 i , c = −2 3 i c = 2 3 i , c = −2 3 i

c = 2 6 i , c = −2 6 i c = 2 6 i , c = −2 6 i

x = 2 10 , x = −2 10 x = 2 10 , x = −2 10

y = 2 7 , y = −2 7 y = 2 7 , y = −2 7

r = 6 5 5 , r = − 6 5 5 r = 6 5 5 , r = − 6 5 5

t = 8 3 3 , t = − 8 3 3 t = 8 3 3 , t = − 8 3 3

a = 3 + 3 2 , a = 3 − 3 2 a = 3 + 3 2 , a = 3 − 3 2

b = −2 + 2 10 , b = −2 − 2 10 b = −2 + 2 10 , b = −2 − 2 10

x = 1 2 + 5 2 x = 1 2 + 5 2 , x = 1 2 − 5 2 x = 1 2 − 5 2

y = − 3 4 + 7 4 , y = − 3 4 − 7 4 y = − 3 4 + 7 4 , y = − 3 4 − 7 4

a = 5 + 2 5 , a = 5 − 2 5 a = 5 + 2 5 , a = 5 − 2 5

b = −3 + 4 2 , b = −3 − 4 2 b = −3 + 4 2 , b = −3 − 4 2

r = − 4 3 + 2 2 i 3 , r = − 4 3 − 2 2 i 3 r = − 4 3 + 2 2 i 3 , r = − 4 3 − 2 2 i 3

t = 4 + 10 i 2 , t = 4 − 10 i 2 t = 4 + 10 i 2 , t = 4 − 10 i 2

m = 7 3 , m = −1 m = 7 3 , m = −1

n = − 3 4 , n = − 7 4 n = − 3 4 , n = − 7 4

ⓐ ( a − 10 ) 2 ( a − 10 ) 2 ⓑ ( b − 5 2 ) 2 ( b − 5 2 ) 2 ⓒ ( p + 1 8 ) 2 ( p + 1 8 ) 2

ⓐ ( b − 2 ) 2 ( b − 2 ) 2 ⓑ ( n + 13 2 ) 2 ( n + 13 2 ) 2 ⓒ ( q − 1 3 ) 2 ( q − 1 3 ) 2

x = −5 , x = −1 x = −5 , x = −1

y = 1 , y = 9 y = 1 , y = 9

y = 5 + 15 i , y = 5 − 15 i y = 5 + 15 i , y = 5 − 15 i

z = −4 + 3 i , z = −4 − 3 i z = −4 + 3 i , z = −4 − 3 i

x = 8 + 4 3 , x = 8 − 4 3 x = 8 + 4 3 , x = 8 − 4 3

y = −4 + 3 3 , y = −4 − 3 3 y = −4 + 3 3 , y = −4 − 3 3

a = −7 , a = 3 a = −7 , a = 3

b = −10 , b = 2 b = −10 , b = 2

p = 5 2 + 61 2 , p = 5 2 − 61 2 p = 5 2 + 61 2 , p = 5 2 − 61 2

q = 7 2 + 37 2 , q = 7 2 − 37 2 q = 7 2 + 37 2 , q = 7 2 − 37 2

c = −9 , c = 3 c = −9 , c = 3

d = 11 , d = −7 d = 11 , d = −7

m = −7 , m = −1 m = −7 , m = −1

n = −2 , n = 8 n = −2 , n = 8

r = − 7 3 , r = 3 r = − 7 3 , r = 3

t = − 5 2 , t = 2 t = − 5 2 , t = 2

x = − 3 8 + 41 8 , x = − 3 8 − 41 8 x = − 3 8 + 41 8 , x = − 3 8 − 41 8

y = 5 3 + 10 3 , y = 5 3 − 10 3 y = 5 3 + 10 3 , y = 5 3 − 10 3

y = 1 , y = 2 3 y = 1 , y = 2 3

z = 1 , z = − 3 2 z = 1 , z = − 3 2

a = −3 , a = 5 a = −3 , a = 5

b = −6 , b = −4 b = −6 , b = −4

m = −6 + 15 3 , m = −6 − 15 3 m = −6 + 15 3 , m = −6 − 15 3

n = −2 + 2 6 5 , n = −2 − 2 6 5 n = −2 + 2 6 5 , n = −2 − 2 6 5

a = 1 4 + 31 4 i , a = 1 4 − 31 4 i a = 1 4 + 31 4 i , a = 1 4 − 31 4 i

b = − 1 5 + 19 5 i , b = − 1 5 − 19 5 i b = − 1 5 + 19 5 i , b = − 1 5 − 19 5 i

x = −1 + 6 , x = −1 − 6 x = −1 + 6 , x = −1 − 6

y = 1 + 2 , y = 1 − 2 y = 1 + 2 , y = 1 − 2

c = 2 + 7 3 , c = 2 − 7 3 c = 2 + 7 3 , c = 2 − 7 3

d = 9 + 33 4 , d = 9 − 33 4 d = 9 + 33 4 , d = 9 − 33 4

r = −5 r = −5

t = 4 5 t = 4 5

ⓐ 2 complex solutions; ⓑ 2 real solutions; ⓒ 1 real solution

ⓐ 2 real solutions; ⓑ 2 complex solutions; ⓒ 1 real solution

ⓐ factoring; ⓑ Square Root Property; ⓒ Quadratic Formula

ⓐ Quadratic Forumula; ⓑ Factoring or Square Root Property ⓒ Square Root Property

x = 2 , x = − 2 , x = 2 , x = −2 x = 2 , x = − 2 , x = 2 , x = −2

x = 7 , x = − 7 , x = 2 , x = −2 x = 7 , x = − 7 , x = 2 , x = −2

x = 3 , x = 1 x = 3 , x = 1

y = −1 , y = 1 y = −1 , y = 1

x = 9 , x = 16 x = 9 , x = 16

x = 4 , x = 16 x = 4 , x = 16

x = −8 , x = 343 x = −8 , x = 343

x = 81 , x = 625 x = 81 , x = 625

x = 4 3 x = 2 x = 4 3 x = 2

x = 2 5 , x = 3 4 x = 2 5 , x = 3 4

The two consecutive odd integers whose product is 99 are 9, 11, and −9, −11

The two consecutive even integers whose product is 128 are 12, 14 and −12, −14.

The height of the triangle is 12 inches and the base is 76 inches.

The height of the triangle is 11 feet and the base is 20 feet.

The length of the garden is approximately 18 feet and the width 11 feet.

The length of the tablecloth is approximatel 11.8 feet and the width 6.8 feet.

The length of the flag pole’s shadow is approximately 6.3 feet and the height of the flag pole is 18.9 feet.

The distance between the opposite corners is approximately 7.2 feet.

The arrow will reach 180 feet on its way up after 3 seconds and again on its way down after approximately 3.8 seconds.

The ball will reach 48 feet on its way up after approximately .6 second and again on its way down after approximately 5.4 seconds.

The speed of the jet stream was 100 mph.

The speed of the jet stream was 50 mph.

Press #1 would take 12 hours, and Press #2 would take 6 hours to do the job alone.

The red hose take 6 hours and the green hose take 3 hours alone.

ⓐ up; ⓑ down

ⓐ down; ⓑ up

ⓐ x = 2 ; x = 2 ; ⓑ ( 2 , −7 ) ( 2 , −7 )

ⓐ x = 1 ; x = 1 ; ⓑ ( 1 , −5 ) ( 1 , −5 )

y -intercept: ( 0 , −8 ) ( 0 , −8 ) x -intercepts ( −4 , 0 ) , ( 2 , 0 ) ( −4 , 0 ) , ( 2 , 0 )

y -intercept: ( 0 , −12 ) ( 0 , −12 ) x -intercepts ( −2 , 0 ) , ( 6 , 0 ) ( −2 , 0 ) , ( 6 , 0 )

y -intercept: ( 0 , 4 ) ( 0 , 4 ) no x -intercept

y -intercept: ( 0 , −5 ) ( 0 , −5 ) x -intercepts ( −1 , 0 ) , ( 5 , 0 ) ( −1 , 0 ) , ( 5 , 0 )

The minimum value of the quadratic function is −4 and it occurs when x = 4.

The maximum value of the quadratic function is 5 and it occurs when x = 2.

It will take 4 seconds for the stone to reach its maximum height of 288 feet.

It will 6.5 seconds for the rocket to reach its maximum height of 676 feet.

ⓑ The graph of g ( x ) = x 2 + 1 g ( x ) = x 2 + 1 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 1 unit. The graph of h ( x ) = x 2 − 1 h ( x ) = x 2 − 1 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted down 1 unit.

ⓑ The graph of h ( x ) = x 2 + 6 h ( x ) = x 2 + 6 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 6 units. The graph of h ( x ) = x 2 − 6 h ( x ) = x 2 − 6 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted down 6 units.

ⓑ The graph of g ( x ) = ( x + 2 ) 2 g ( x ) = ( x + 2 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 2 units. The graph of h ( x ) = ( x − 2 ) 2 h ( x ) = ( x − 2 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shift right 2 units.

ⓑ The graph of g ( x ) = ( x + 5 ) 2 g ( x ) = ( x + 5 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 5 units. The graph of h ( x ) = ( x − 5 ) 2 h ( x ) = ( x − 5 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted right 5 units.

f ( x ) = −4 ( x + 1 ) 2 + 5 f ( x ) = −4 ( x + 1 ) 2 + 5

f ( x ) = 2 ( x − 2 ) 2 − 5 f ( x ) = 2 ( x − 2 ) 2 − 5

ⓐ f ( x ) = 3 ( x − 1 ) 2 + 2 f ( x ) = 3 ( x − 1 ) 2 + 2 ⓑ

ⓐ f ( x ) = −2 ( x − 2 ) 2 + 1 f ( x ) = −2 ( x − 2 ) 2 + 1 ⓑ

f ( x ) = ( x − 3 ) 2 − 4 f ( x ) = ( x − 3 ) 2 − 4

f ( x ) = ( x + 3 ) 2 − 1 f ( x ) = ( x + 3 ) 2 − 1

ⓑ ( −4 , −2 ) ( −4 , −2 )

ⓑ ( − ∞ , 2 ] ∪ [ 6 , ∞ ) ( − ∞ , 2 ] ∪ [ 6 , ∞ )

ⓑ ( −1 , 5 ) ( −1 , 5 )

ⓑ ( − ∞ , 2 ] ∪ [ 8 , ∞ ) ( − ∞ , 2 ] ∪ [ 8 , ∞ )

( − ∞ , −4 ] ∪ [ 2 , ∞ ) ( − ∞ , −4 ] ∪ [ 2 , ∞ )

[ −3 , 5 ] [ −3 , 5 ]

[ −1 − 2 , −1 + 2 ] [ −1 − 2 , −1 + 2 ]

( − ∞ , 4 − 2 ) ∪ ( 4 + 2 , ∞ ) ( − ∞ , 4 − 2 ) ∪ ( 4 + 2 , ∞ )

ⓐ ( − ∞ , ∞ ) ( − ∞ , ∞ ) ⓑ no solution

ⓐ no solution ⓑ ( − ∞ , ∞ ) ( − ∞ , ∞ )

Section 9.1 Exercises

a = ± 7 a = ± 7

r = ± 2 6 r = ± 2 6

u = ± 10 3 u = ± 10 3

m = ± 3 m = ± 3

x = ± 6 x = ± 6

x = ± 5 i x = ± 5 i

x = ± 3 7 i x = ± 3 7 i

x = ± 9 x = ± 9

a = ± 2 5 a = ± 2 5

p = ± 4 7 7 p = ± 4 7 7

y = ± 4 10 5 y = ± 4 10 5

u = 14 , u = −2 u = 14 , u = −2

m = 6 ± 2 5 m = 6 ± 2 5

r = 1 2 ± 3 2 r = 1 2 ± 3 2

y = − 2 3 ± 2 2 9 y = − 2 3 ± 2 2 9

a = 7 ± 5 2 a = 7 ± 5 2

x = −3 ± 2 2 x = −3 ± 2 2

c = − 1 5 ± 3 3 5 i c = − 1 5 ± 3 3 5 i

x = 3 4 ± 7 2 i x = 3 4 ± 7 2 i

m = 2 ± 2 2 m = 2 ± 2 2

x = 3 + 2 3 , x = 3 − 2 3 x = 3 + 2 3 , x = 3 − 2 3

x = − 3 5 , x = 9 5 x = − 3 5 , x = 9 5

x = − 7 6 , x = 11 6 x = − 7 6 , x = 11 6

r = ± 4 r = ± 4

a = 4 ± 2 7 a = 4 ± 2 7

w = 1 , w = 5 3 w = 1 , w = 5 3

a = ± 3 2 a = ± 3 2

p = 1 3 ± 7 3 p = 1 3 ± 7 3

m = ± 2 2 i m = ± 2 2 i

u = 7 ± 6 2 u = 7 ± 6 2

m = 4 ± 2 3 m = 4 ± 2 3

x = −3 , x = −7 x = −3 , x = −7

c = ± 5 6 6 c = ± 5 6 6

x = 6 ± 2 i x = 6 ± 2 i

Answers will vary.

Section 9.2 Exercises

ⓐ ( m − 12 ) 2 ( m − 12 ) 2 ⓑ ( x − 11 2 ) 2 ( x − 11 2 ) 2 ⓒ ( p − 1 6 ) 2 ( p − 1 6 ) 2

ⓐ ( p − 11 ) 2 ( p − 11 ) 2 ⓑ ( y + 5 2 ) 2 ( y + 5 2 ) 2 ⓒ ( m + 1 5 ) 2 ( m + 1 5 ) 2

u = −3 , u = 1 u = −3 , u = 1

x = −1 , x = 21 x = −1 , x = 21

m = −2 ± 2 10 i m = −2 ± 2 10 i

r = −3 ± 2 i r = −3 ± 2 i

a = 5 ± 2 5 a = 5 ± 2 5

x = − 5 2 ± 33 2 x = − 5 2 ± 33 2

u = 1 , u = 13 u = 1 , u = 13

r = −2 , r = 6 r = −2 , r = 6

v = 9 2 ± 89 2 v = 9 2 ± 89 2

x = 5 ± 30 x = 5 ± 30

x = −7 , x = 3 x = −7 , x = 3

m = −11 , m = 1 m = −11 , m = 1

n = 1 ± 14 n = 1 ± 14

c = −2 , c = 3 2 c = −2 , c = 3 2

x = −5 , x = 3 2 x = −5 , x = 3 2

p = − 7 4 ± 161 4 p = − 7 4 ± 161 4

x = 3 10 ± 191 10 i x = 3 10 ± 191 10 i

Section 9.3 Exercises

m = −1 , m = 3 4 m = −1 , m = 3 4

p = 1 2 , p = 3 p = 1 2 , p = 3

p = −4 , p = −3 p = −4 , p = −3

r = −3 , r = 11 r = −3 , r = 11

u = −7 ± 73 6 u = −7 ± 73 6

a = 3 ± 3 2 a = 3 ± 3 2

x = −4 ± 2 5 x = −4 ± 2 5

y = −2 , y = 1 3 y = −2 , y = 1 3

x = − 3 4 ± 15 4 i x = − 3 4 ± 15 4 i

x = 3 8 ± 7 8 i x = 3 8 ± 7 8 i

v = 2 ± 2 13 v = 2 ± 2 13

y = −4 , y = 7 y = −4 , y = 7

b = −2 ± 11 6 b = −2 ± 11 6

c = − 3 4 c = − 3 4

q = − 3 5 q = − 3 5

ⓐ no real solutions no real solutions ⓑ 1 1 ⓒ 2 2

ⓐ 1 1 ⓑ no real solutions no real solutions ⓒ 2 2

ⓐ factor factor ⓑ square root square root ⓒ Quadratic Formula Quadratic Formula

ⓐ Quadratic Formula Quadratic Formula ⓑ square root square root ⓒ factor factor

Section 9.4 Exercises

x = ± 3 , x = ± 2 x = ± 3 , x = ± 2

x = ± 15 , x = ± 2 i x = ± 15 , x = ± 2 i

x = ± 1 , x = ± 6 2 x = ± 1 , x = ± 6 2

x = ± 3 , x = ± 2 2 x = ± 3 , x = ± 2 2

x = −1 , x = 12 x = −1 , x = 12

x = − 5 3 , x = 0 x = − 5 3 , x = 0

x = 0 , x = ± 3 x = 0 , x = ± 3

x = ± 11 2 , x = ± 7 x = ± 11 2 , x = ± 7

x = 25 x = 25

x = 4 x = 4

x = 1 4 x = 1 4

x = 1 25 , x = 9 4 x = 1 25 , x = 9 4

x = −1 , x = −512 x = −1 , x = −512

x = 8 , x = −216 x = 8 , x = −216

x = 27 8 , x = − 64 27 x = 27 8 , x = − 64 27

x = 27 512 , x = 125 x = 27 512 , x = 125

x = 1 , x = 49 x = 1 , x = 49

x = −2 , x = − 3 5 x = −2 , x = − 3 5

x = −2 , x = 4 3 x = −2 , x = 4 3

Section 9.5 Exercises

Two consecutive odd numbers whose product is 255 are 15 and 17, and −15 and −17.

The first and second consecutive odd numbers are 24 and 26, and −26 and −24.

Two consecutive odd numbers whose product is 483 are 21 and 23, and −21 and −23.

The width of the triangle is 5 inches and the height is 18 inches.

The base is 24 feet and the height of the triangle is 10 feet.

The length of the driveway is 15.0 feet and the width is 3.3 feet.

The length of table is 8 feet and the width is 3 feet.

The length of the legs of the right triangle are 3.2 and 9.6 cm.

The length of the diagonal fencing is 7.3 yards.

The ladder will reach 24.5 feet on the side of the house.

The arrow will reach 400 feet on its way up in 2.8 seconds and on the way down in 11 seconds.

The bullet will take 70 seconds to hit the ground.

The speed of the wind was 49 mph.

The speed of the current was 4.3 mph.

The less experienced painter takes 6 hours and the experienced painter takes 3 hours to do the job alone.

Machine #1 takes 3.6 hours and Machine #2 takes 4.6 hours to do the job alone.

Section 9.6 Exercises

ⓐ down ⓑ up

ⓐ x = −4 x = −4 ; ⓑ ( −4 , −17 ) ( −4 , −17 )

ⓐ x = 1 x = 1 ; ⓑ ( 1 , 2 ) ( 1 , 2 )

y -intercept: ( 0 , 6 ) ; ( 0 , 6 ) ; x -intercept ( −1 , 0 ) , ( −6 , 0 ) ( −1 , 0 ) , ( −6 , 0 )

y -intercept: ( 0 , 12 ) ; ( 0 , 12 ) ; x -intercept ( −2 , 0 ) , ( −6 , 0 ) ( −2 , 0 ) , ( −6 , 0 )

y -intercept: ( 0 , −19 ) ; ( 0 , −19 ) ; x -intercept: none

y -intercept: ( 0 , 13 ) ; ( 0 , 13 ) ; x -intercept: none

y -intercept: ( 0 , −16 ) ; ( 0 , −16 ) ; x -intercept ( 5 2 , 0 ) ( 5 2 , 0 )

y -intercept: ( 0 , 9 ) ; ( 0 , 9 ) ; x -intercept ( −3 , 0 ) ( −3 , 0 )

The minimum value is − 9 8 − 9 8 when x = − 1 4 . x = − 1 4 .

The maximum value is 6 when x = 3.

The maximum value is 16 when x = 0.

In 5.3 sec the arrow will reach maximum height of 486 ft.

In 3.4 seconds the ball will reach its maximum height of 185.6 feet.

20 computers will give the maximum of $400 in receipts.

He will be able to sell 35 pairs of boots at the maximum revenue of $1,225.

The length of the side along the river of the corral is 120 feet and the maximum area is 7,200 square feet.

The maximum area of the patio is 800 feet.

Section 9.7 Exercises

ⓑ The graph of g ( x ) = x 2 + 4 g ( x ) = x 2 + 4 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted up 4 units. The graph of h ( x ) = x 2 − 4 h ( x ) = x 2 − 4 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shift down 4 units.

ⓑ The graph of g ( x ) = ( x − 3 ) 2 g ( x ) = ( x − 3 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted right 3 units. The graph of h ( x ) = ( x + 3 ) 2 h ( x ) = ( x + 3 ) 2 is the same as the graph of f ( x ) = x 2 f ( x ) = x 2 but shifted left 3 units.

f ( x ) = −3 ( x + 2 ) 2 + 7 f ( x ) = −3 ( x + 2 ) 2 + 7

f ( x ) = 3 ( x + 1 ) 2 − 4 f ( x ) = 3 ( x + 1 ) 2 − 4

ⓐ f ( x ) = ( x + 3 ) 2 − 4 f ( x ) = ( x + 3 ) 2 − 4 ⓑ

ⓐ f ( x ) = ( x + 2 ) 2 − 1 f ( x ) = ( x + 2 ) 2 − 1 ⓑ

ⓐ f ( x ) = ( x − 3 ) 2 + 6 f ( x ) = ( x − 3 ) 2 + 6 ⓑ

ⓐ f ( x ) = − ( x − 4 ) 2 + 0 f ( x ) = − ( x − 4 ) 2 + 0 ⓑ

ⓐ f ( x ) = − ( x + 2 ) 2 + 6 f ( x ) = − ( x + 2 ) 2 + 6 ⓑ

ⓐ f ( x ) = 5 ( x − 1 ) 2 + 3 f ( x ) = 5 ( x − 1 ) 2 + 3 ⓑ

ⓐ f ( x ) = 2 ( x − 1 ) 2 − 1 f ( x ) = 2 ( x − 1 ) 2 − 1 ⓑ

ⓐ f ( x ) = −2 ( x − 2 ) 2 − 2 f ( x ) = −2 ( x − 2 ) 2 − 2 ⓑ

ⓐ f ( x ) = 2 ( x + 1 ) 2 + 4 f ( x ) = 2 ( x + 1 ) 2 + 4 ⓑ

ⓐ f ( x ) = − ( x − 1 ) 2 − 3 f ( x ) = − ( x − 1 ) 2 − 3 ⓑ

f ( x ) = ( x + 1 ) 2 − 5 f ( x ) = ( x + 1 ) 2 − 5

f ( x ) = 2 ( x − 1 ) 2 − 3 f ( x ) = 2 ( x − 1 ) 2 − 3

Section 9.8 Exercises

ⓑ ( − ∞ , −5 ) ∪ ( −1 , ∞ ) ( − ∞ , −5 ) ∪ ( −1 , ∞ )

ⓑ [ −3 , −1 ] [ −3 , −1 ]

ⓑ ( − ∞ , −6 ] ∪ [ 3 , ∞ ) ( − ∞ , −6 ] ∪ [ 3 , ∞ )

ⓑ [ −3 , 4 ] [ −3 , 4 ]

( − ∞ , −4 ] ∪ [ 1 , ∞ ) ( − ∞ , −4 ] ∪ [ 1 , ∞ )

( 2 , 5 ) ( 2 , 5 )

( − ∞ , −5 ) ∪ ( −3 , ∞ ) ( − ∞ , −5 ) ∪ ( −3 , ∞ )

[ 2 − 2 , 2 + 2 ] [ 2 − 2 , 2 + 2 ]

( − ∞ , 5 − 6 ) ∪ ( 5 + 6 , ∞ ) ( − ∞ , 5 − 6 ) ∪ ( 5 + 6 , ∞ )

( − ∞ , − 5 2 ] ∪ [ − 2 3 , ∞ ) ( − ∞ , − 5 2 ] ∪ [ − 2 3 , ∞ )

[ − 1 2 , 4 ] [ − 1 2 , 4 ]

( − ∞ , ∞ ) . ( − ∞ , ∞ ) .

no solution

Review Exercises

y = ± 12 y = ± 12

a = ± 5 a = ± 5

r = ± 4 2 i r = ± 4 2 i

w = ± 5 3 w = ± 5 3

p = −1 , 9 p = −1 , 9

x = 1 4 ± 3 4 x = 1 4 ± 3 4

n = 4 ± 10 2 n = 4 ± 10 2

n = −5 ± 2 3 n = −5 ± 2 3

( x + 11 ) 2 ( x + 11 ) 2

( a − 3 2 ) 2 ( a − 3 2 ) 2

d = −13 , −1 d = −13 , −1

m = −3 ± 10 i m = −3 ± 10 i

v = 7 ± 3 2 v = 7 ± 3 2

m = −9 , −1 m = −9 , −1

a = 3 2 ± 41 2 a = 3 2 ± 41 2

u = −6 ± 2 2 u = −6 ± 2 2

p = 0 , 6 p = 0 , 6

y = − 1 2 , 2 y = − 1 2 , 2

c = − 1 3 ± 2 7 3 c = − 1 3 ± 2 7 3

x = 3 2 ± 1 2 i x = 3 2 ± 1 2 i

x = 1 4 , 1 x = 1 4 , 1

r = −6 , 7 r = −6 , 7

v = −1 ± 21 8 v = −1 ± 21 8

m = −4 ± 10 3 m = −4 ± 10 3

a = 5 12 ± 23 12 i a = 5 12 ± 23 12 i

u = 5 ± 21 u = 5 ± 21

p = 4 ± 5 5 p = 4 ± 5 5

c = − 1 2 c = − 1 2

ⓐ 1 ⓑ 2 ⓒ 2 ⓓ 2

ⓐ factor ⓑ Quadratic Formula ⓒ square root

x = ± 2 , x = ± 2 3 x = ± 2 , x = ± 2 3

x = ± 1 , x = ± 1 2 x = ± 1 , x = ± 1 2

x = 16 x = 16

x = 64 , x = 216 x = 64 , x = 216

Two consecutive even numbers whose product is 624 are 24 and 26, and −24 and −26.

The height is 14 inches and the width is 10 inches.

The length of the diagonal is 3.6 feet.

The width of the serving table is 4.7 feet and the length is 16.1 feet.

The speed of the wind was 30 mph.

One man takes 3 hours and the other man 6 hours to finish the repair alone.

ⓐ up ⓑ down

x = 2 ; ( 2 , −7 ) x = 2 ; ( 2 , −7 )

y : ( 0 , 15 ) x : ( 3 , 0 ) , ( 5 , 0 ) y : ( 0 , 15 ) x : ( 3 , 0 ) , ( 5 , 0 )

y : ( 0 , −46 ) x : none y : ( 0 , −46 ) x : none

y : ( 0 , −64 ) x : ( −8 , 0 ) y : ( 0 , −64 ) x : ( −8 , 0 )

The maximum value is 2 when x = 2.

The length adjacent to the building is 90 feet giving a maximum area of 4,050 square feet.

f ( x ) = 2 ( x − 1 ) 2 − 6 f ( x ) = 2 ( x − 1 ) 2 − 6

ⓐ f ( x ) = 3 ( x − 1 ) 2 − 4 f ( x ) = 3 ( x − 1 ) 2 − 4 ⓑ

ⓐ f ( x ) = −3 ( x + 2 ) 2 + 7 f ( x ) = −3 ( x + 2 ) 2 + 7 ⓑ

ⓑ ( − ∞ , −2 ) ∪ ( 3 , ∞ ) ( − ∞ , −2 ) ∪ ( 3 , ∞ )

[ −2 , 1 ] [ −2 , 1 ]

( 2 , 4 ) ( 2 , 4 )

[ 3 − 5 , 3 + 5 ] [ 3 − 5 , 3 + 5 ]

Practice Test

w = −2 , w = −8 w = −2 , w = −8

m = 1 , m = 3 2 m = 1 , m = 3 2

y = 2 3 y = 2 3

y = 1 , y = −27 y = 1 , y = −27

ⓐ down ⓑ x = −4 x = −4 ⓒ ( −4 , 0 ) ( −4 , 0 ) ⓓ y : ( 0 , 16 ) ; x : ( −4 , 0 ) y : ( 0 , 16 ) ; x : ( −4 , 0 ) ⓔ minimum value of −4 −4 when x = 0 x = 0

( − ∞ , − 5 2 ) ∪ ( 2 , ∞ ) ( − ∞ , − 5 2 ) ∪ ( 2 , ∞ )

The diagonal is 3.8 units long.

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• Book title: Intermediate Algebra
• Publication date: Mar 14, 2017
• Location: Houston, Texas
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• Section URL: https://openstax.org/books/intermediate-algebra/pages/chapter-9

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All Things Algebra®

Algebra 2 Unit 4: Quadratic Equations & Complex Numbers

This unit includes 86 pages of guided notes, homework assignments, three quizzes, a study guide, and a unit test that cover the topics listed in the description below.

• Description
• Additional Information
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This unit contains the following topics:

• Roots of a Quadratic Equation; Solving Quadratics by Graphing • Factoring Review • Solving Quadratics by Factoring • Factored Form/Vertex Form/Standard Form of a Quadratic Equation • Simplifying Radicals Review • Solving Quadratics by Square Roots • Imaginary Numbers • Solving Square Roots Problems with Imaginary Solutions • Operations with Complex Numbers • Organizing the Real and Complex Numbers • Properties with Complex Numbers • Solving Quadratics by Completing the Square • Solving Quadratics by The Quadratic Formula • The Discriminant • Review of all Methods; Choosing the Best Method • Geometric and Consecutive Integer Applications • Projectile Motion • Quadratic Regression • Solving Nonlinear Systems of Equations (Linear-Quadratic and Quadratic-Quadratic) graphically • Solving Nonlinear Systems of Equations (Linear-Quadratic and Quadratic-Quadratic) algebraically

This unit does not contain activities.

This is the guided notes, homework assignments, quizzes, study guide, and unit test only.  For suggested activities to go with this unit, check out the ATA Activity Alignment Guides .

This resource is included in the following bundle(s):

Algebra 2 Curriculum

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This purchase includes a single non-transferable license, meaning it is for one teacher only for personal use in their classroom and can not be passed from one teacher to another.  No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses.  A t ransferable license is not available for this resource.

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9.4E: Exercises

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Practice Makes Perfect

Exercises 1 - 32: solve quadratic equations using the quadratic formula.

In the following exercises, solve by using the Quadratic Formula.

1. \(4 m^{2}+m-3=0\)

2. \(4 n^{2}-9 n+5=0\)

3. \(2 p^{2}-7 p+3=0\)

4. \(3 q^{2}+8 q-3=0\)

5. \(p^{2}+7 p+12=0\)

6. \(q^{2}+3 q-18=0\)

7. \(r^{2}-8 r=33\)

8. \(t^{2}+13 t=-40\)

9. \(3 u^{2}+7 u-2=0\)

10. \(2 p^{2}+8 p+5=0\)

11. \(2 a^{2}-6 a+3=0\)

12. \(5 b^{2}+2 b-4=0\)

13. \(x^{2}+8 x-4=0\)

14. \(y^{2}+4 y-4=0\)

15. \(3 y^{2}+5 y-2=0\)

16. \(6 x^{2}+2 x-20=0\)

17. \(2 x^{2}+3 x+3=0\)

18. \(2 x^{2}-x+1=0\)

19. \(8 x^{2}-6 x+2=0\)

20. \(8 x^{2}-4 x+1=0\)

21. \((v+1)(v-5)-4=0\)

22. \((x+1)(x-3)=2\)

23. \((y+4)(y-7)=18\)

24. \((x+2)(x+6)=21\)

25. \(\dfrac{1}{4} m^{2}+\dfrac{1}{12} m=\dfrac{1}{3}\)

26. \(\dfrac{1}{3} n^{2}+n=-\dfrac{1}{2}\)

27. \(\dfrac{3}{4} b^{2}+\dfrac{1}{2} b=\dfrac{3}{8}\)

28. \(\dfrac{1}{9} c^{2}+\dfrac{2}{3} c=3\)

29. \(16 c^{2}+24 c+9=0\)

30. \(25 d^{2}-60 d+36=0\)

31. \(25 q^{2}+30 q+9=0\)

32. \(16 y^{2}+8 y+1=0\)

1. \(m=-1, m=\dfrac{3}{4}\)

3. \(p=\dfrac{1}{3}, p=2\)

5. \(p=-4, p=-3\)

7. \(r=-3, r=11\)

9. \(u=\dfrac{-7 \pm \sqrt{73}}{6}\)

11. \(a=\dfrac{3 \pm \sqrt{3}}{2}\)

13. \(x=-4 \pm 2 \sqrt{5}\)

15. \(y=-\dfrac{2}{3}, y=-1\)

17. \(x=-\dfrac{3}{4} \pm \dfrac{\sqrt{15}}{4} i\)

19. \(x=\dfrac{3}{8} \pm \dfrac{\sqrt{7}}{8} i\)

21. \(v=2 \pm 2 \sqrt{2}\)

23. \(y=-4, y=7\)

25. \(m=1, m=\dfrac{-4}{3}\)

27. \(b=\dfrac{-2 \pm \sqrt{22}}{6}\)

29. \(c=-\dfrac{3}{4}\)

31. \(q=-\dfrac{3}{5}\)

ExerciseS 33 - 36 Use the Discriminant to Predict the Number of Real Solutions of a Quadratic Equation

In the following exercises, determine the number of real solutions for each quadratic equation.

• \(4 x^{2}-5 x+16=0\)
• \(36 y^{2}+36 y+9=0\)
• \(6 m^{2}+3 m-5=0\)
• \(9 v^{2}-15 v+25=0\)
• \(100 w^{2}+60 w+9=0\)
• \(5 c^{2}+7 c-10=0\)
• \(r^{2}+12 r+36=0\)
• \(8 t^{2}-11 t+5=0\)
• \(3 v^{2}-5 v-1=0\)
• \(25 p^{2}+10 p+1=0\)
• \(7 q^{2}-3 q-6=0\)
• \(7 y^{2}+2 y+8=0\)

33. a. no real solutions b. \(1\) c. \(2\)

35. a. \(1\) b. no real solutions c. \(2\)

ExerciseS 37 - 40: Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

• \(x^{2}-5 x-24=0\)
• \((y+5)^{2}=12\)
• \(14 m^{2}+3 m=11\)
• \((8 v+3)^{2}=81\)
• \(w^{2}-9 w-22=0\)
• \(4 n^{2}-10=6\)
• \(6 a^{2}+14=20\)
• \(\left(x-\dfrac{1}{4}\right)^{2}=\dfrac{5}{16}\)
• \(y^{2}-2 y=8\)
• \(8 b^{2}+15 b=4\)
• \(\dfrac{5}{9} v^{2}-\dfrac{2}{3} v=1\)
• \(\left(w+\dfrac{4}{3}\right)^{2}=\dfrac{2}{9}\)

37. a. Factor b. Square Root c. Quadratic Formula

39. a. Quadratic Formula b. Square Root c. Factor

ExerciseS 41 - 42: Writing Exercises

• by completing the square
• using the Quadratic Formula
• Which method do you prefer? Why?

41. Answers will vary

a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

b. What does this checklist tell you about your mastery of this section? What steps will you take to improve?