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Unit 9 – Quadratics 1
Name: ____________________ Teacher: _____________ Per: ___
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
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