Unit 9 – Quadratics 1

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Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

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Unit 9

Unit 10

– Unit 9b – [Quadratic Equations]

Unit 9 – Quadratics 2

To be a Successful Algebra class,

TIGERs will show…

#TENACITY during our practice, have…

I attempt all practice I attempt all homework I never give up when I don’t understand

#INTEGRITY as we help others with their work, maintain a…

I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them

#GO-FOR-IT attitude, continually…

I write down all notes, even if I’m confused I remain positive about my goals I treat each day as a chance to reset

#ENCOURAGE each other to succeed as a team, and always…

I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up

#REACH-OUT and ask for help when we need it!

I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to

Unit 9 – Quadratics 3

Unit Calendar

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

March 16 17 18 19 20

Domain and Range for Discrete and

Continuous Functions

Introduce Quadratic Graph and

Transformations

Identify Key Features from the Graph QUIZ

Identify Key Features from the Table

Identify Key Features from the Calculator

23 24 25 26 27

Mixed Practice Applications

Review

TEST A

DLA

30 31 April 1 2 3

English I EOC

Solve by Factoring Solve by Factoring Solve by Quadratic Formula

Holiday

6 7 8 9 10

Solve all 4 Ways

Solve Practice

QUIZ

Classify Functions Review

TEST B

Essential Questions

What are the similarities and differences between a linear and quadratic function?

What do zeroes, solutions, roots, and x-intercepts have in common? How do they differ?

Unit 9 – Quadratics 4

Critical Vocabulary

Quadratic

Parabola

Roots

Zeroes

x-intercepts

Solutions

Vertex

Axis of Symmetry

Unit 9 – Quadratics 5

Quadratics: Solve by Factoring

𝑥2 − 𝑥 − 6 = 0

x f(x)

Examples:

𝑥2 + 2𝑥 − 3 = 0

𝑎2 − 13𝑎 − 30 = 0

𝑥2 − 8𝑥 = −12

𝑥2 + 30 = 11𝑥

Unit 9 – Quadratics 6

Practice:

𝑏2 + 8𝑏 + 7 = 0

𝑚2 + 𝑚 − 90 = 0

𝑛2 + 4𝑛 = 12

𝑏2 + 64 = −16𝑏

𝑛2 − 11𝑛 = −10

𝑛2 − 10𝑛 = −9

𝑥2 + 8𝑥 − 48 = 0

𝑥2 + 𝑥 = 6

Unit 9 – Quadratics 7

Quadratics: Solve by Factoring Cont…

2𝑥2 + 7𝑥 − 4 = 0

x f(x)

Examples:

3𝑥2 + 17𝑥 + 20 = 0

6x2 – 7x – 3

3𝑥2 + 𝑥 = 4

4𝑥2 = 9𝑥 + 9

Unit 9 – Quadratics 8

Practice:

7x2 - 5x – 2 = 0

23 17 20x x = 0

3x2 + 14x = -8

2x2 + 4 = 6x

2x2 + 11x = -14

24 15 16x x

26 19 10x x = 0

24 9 9x x

Unit 9 – Quadratics 9

Unit 9 – Quadratics 10

Quadratics: The Quadratic Formula

Graphing

Factoring

x2 – 2x – 3

Quadratic Formula

Put in the form ax2 + bx + c = 0

Identify the values for a,b,c

Plug in and evaluate

Examples:

𝑥2 − 2𝑥 − 3 = 0

2𝑥2 = −7𝑥 + 15

𝑎2 + 2𝑎 = −1

ℎ2 + ℎ − 2 = −2ℎ

Unit 9 – Quadratics 11

Practice:

𝑚2 − 14 = 5𝑚

𝑏2 − 4𝑏 = −4

2𝑥2 − 3𝑥 = 5

𝑥2 + 4𝑥 − 3 = 0

3𝑥2 + 7𝑥 = 1

𝑥2 + 4 = −2𝑥

***Note: After you simplify the square root, if your number is negative, we get an error and the answer is No Solution.

Unit 9 – Quadratics 12

Quadratics: Solving Practice

x f(x)

1 2

3

4 5

6

Examples:

Solve by Factoring and Quadratic Formula 𝑓(𝑥) = 𝑥2 + 4𝑥 − 21

Solve by Factoring and Quadratic Formula 𝑦 = 2𝑥2 + 𝑥 − 6

Graphing

Quadratic formula

Factoring

𝑥2 − 6𝑥 + 5 = 0

Table

Unit 9 – Quadratics 13

Practice:

Solve by Quadratic Formula, 𝑏2 + 8𝑏 + 7 = 0

Solve by graphing, 𝑓(𝑥) = 2𝑥2 + 4𝑥 + 3

Solve by Factoring, 𝑛2 + 4𝑛 = 12

Solve by using a table, 𝑓(𝑥) = 𝑥2 + 4𝑥 − 5

x f(x)

-5

-4

-3

-2

-1

0

1

Solve by Quadratic Formula, 𝑥2 + 5𝑥 − 2 = 2𝑥

Solve by Factoring, 2𝑥2 + 7𝑥 = 15

Solve by using a table, 𝑥2 − 12𝑥 = −35

x f(x)

4 5

6

7 8

Solve by graphing 𝑥2 − 2𝑥 − 3 = 0

Unit 9 – Quadratics 14

Unit 9 – Quadratics 15

Unit 9 – Quadratics 16

Quadratics: Classifying Functions

Linear y = x

Quadratic y = x2 Exponential y = 2x

x f(x)

-3

-2

-1

0

1

2

3

x f(x)

-3

-2

-1

0

1

2

3

x f(x)

-3

-2

-1

0

1

2

3

y = mx + b

y = ax2 + bx + c

y = abx Growth b > 1 Decay 0<b<1

First difference is the same

Second difference is the same

Pattern is multiply or divide

Examples:

a b c

x y

-3 31

-2 17

-1 7

0 1

1 -1

2 1

3 7

x y

-3 2

-2 4

-1 8

0 16

1 32

2 64

3 128

x y

-3 -4

-2 -2

-1 0

0 2

1 4

2 6

3 8

Pattern:

Unit 9 – Quadratics 17

Practice: Determine whether the following functions are linear, exponential, quadratic or neither. If they are exponential

identify if they are growth or decay.

X Y

4 7 5 9

6 11

7 13

A function that is decreasing at a constant rate.

X -1 0 1 2 3

Y -4 1 10 23 40

𝑦 = 3 (4

3)

𝑥

𝑦 = 2𝑥2 + 3𝑥 − 5

−3𝑥 = 4𝑦 + 7

X -1 0 1 2 3

Y 7 5 3 5 7

X -1 0 1 2 3

Y 27 9 3 1 1

3

X -1 0 1 2 3

Y 8 4 0 -4 -8

X Y

0 1

1 3

2 9

3 27

4 81

X Y

-2 8

-1 2

0 0

1 2

2 8

X Y

3 -32

4 -18

5 0

6 22

7 48

X Y

-1 12

0 6

1 3

2 1.5

3 .75

X Y

0 2

1 5

2 8

3 11

4 14

X Y

0 -1

1 1

2 7

3 17

4 31

Unit 9 – Quadratics 18

Unit 9 – Quadratics 19