Algebra 2 Goal III: To Use Quadratic Functions, Equations and Inequalities
Learning Outcomes
Differentiated Instructional Activities
3.1 Graph quadratic functions:
Use the Developing Concepts Activity to introduce
Lesson 5.3. An alternative way to approach
Lesson 5.3 is to use the Graphing Calculator
Lesson Opener. Have students copy the
characteristics of the graph of a quadratic function,
and the vertex and intercept forms and
characteristics of the graph the of a quadratic
function on 3X5 index cards. Continue vocabulary
file or algebra glossary. Make sure that English
learners understand parabolas. Students need to
understand that only parabolas that open up or
down are functions. Writing Activity: Have
students explain how to draw the graph of a
quadratic equation that is given in intercept form.
Use the cooperative learning activity and /or
graphing calculator activity.
Vertex form
Intercept form
Standard form
Text Book
References*
Developing
Concepts: p. 249
Chapter Resource Book
References
Warm-Up Exercises:
p. 11
Assessments#
Examples: 1-6,
pp. 250-252
Lesson Opener (Graphing
Calculator): p. 12
Guided Practice:
p. 253, #’s 1-16
Practice A, B, & C:
pp. 15-17
HQ: p. 33^
Practice:
pp. 253-255,
#’s 17-78
(See Assignment
Guide, p. 253)
Reteaching with Practice:
pp. 18-19
Quiz 1: p. 270, #’s 1-3
RS: Quiz 1: p. 50, #’s 1-2^
WT: p. 31^ Prerequisite
Skills Review
WT: p. 32^
Checkpoint Exercises:
pp. 250-252
Cooperative Learning
Activity: p. 21
Real Life Application:
p. 22
Challenge: p. 23
Chapter Reference 5.1
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Graphing Calculator
Activity: pp. 13-14
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
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Learning Outcomes
Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book
References
Assessments#
3.2 Solve quadratic equations
by factoring:
An alternative way to approach Lesson 5.2 is to
use the Visual Approach Lesson Opener. Have
students copy the special factoring patterns, and
the zero product property on 3X5 index cards.
Continue vocabulary file or algebra glossary. Help
English learners distinguish among monomial,
binomial, and trinomial. Provide examples such as
monorail, bicycle, and tricycle. Ask students what
must be true about a quadratic equation before you
can solve it using the zero product property. Give
students much practice with factoring trinomials.
To avoid errors, have students multiply the factors
to make sure the product is the original expression.
Writing Activity: Have students name, give an
example, and describe how to factor the three
special factoring patterns
Use the Developing Concepts Activity to introduce
Lesson 5.3. An alternative way to approach
Lesson 5.3 is to use the Application Lesson
Opener. Have students copy the properties of
square roots on a 3X5 index card. Continue
vocabulary file or algebra glossary. Writing
Activity: Have students write a quadratic equation
that they would solve by finding square roots and
show how to solve it. Then have them explain
why they would chose to solve this equation using
square roots rather than factoring. Have students
do the Using Technology Activity that uses a
graphing calculator to solve quadratic equations
having real number solutions and/or the graphing
calculator activity.
Examples: 1-8,
pp. 256-259
Warm-Up Exercises: p. 26
WT: p. 33^
Lesson Opener (Visual
Approach): p. 27
Checkpoint Exercises:
pp. 257-259
Special patterns
Find zeros of quadratic functions
Chapter Reference 5.2
3.3 Solve quadratic equations
by finding square roots
Chapter Reference 5.3
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Guided Practice:
p. 260, #’s 1-22
Practice:
pp. 260-263,
#’s 23-136
(See Assignment
Guide, p. 260)
Practice A, B, & C: pp. 28-30
Reteaching with Practice:
pp. 31-32
HQ: p. 34^
Quiz 1: p. 270, #’s 4-6
RS: Quiz 1: p. 50, #’s 3-4^
Interdisciplinary Application:
p. 34
Challenge: p. 35
Developing
Concepts: p. 264
Examples: 1-4,
pp. 264-266
Warm-Up Exercises: p. 38
WT: p. 34^
Lesson Opener (Application):
p. 39
Checkpoint Exercises:
pp. 265-266
Practice A, B, & C: pp. 41-43
Guided Practice:
p. 267, #’s 1-18
Practice:
pp. 267-269,
#’s 19-91
(See Assignment
Guide, p. 267)
Using Technology:
p. 271
Reteaching with Practice:
pp. 44-45
HQ: p. 35^
Quiz 1: p. 270, #’s 7-11
RS: Quiz 1: p. 50, #’s 5-7^
Real Life & Math and History
Applications: pp. 47-48
Challenge: p. 49
Graphing Calculator Activity:
p. 40
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
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Learning Outcomes
Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book
References
Assessments#
3.4 Solve quadratic equations
with complex numbers:
An alternative way to approach Lesson 5.4 is to
use the Activity Lesson Opener. Have students
copy the property of the square root of a negative
number, the definition of the absolute value of a
complex number, and how to determine whether
complex numbers belong to the Mandelbrot set on
3X5 index cards. Continue vocabulary file or
algebra glossary. Ask students to describe the
procedure for each of the four basic operations on
complex numbers. Writing Activity: Have
students explain, in one or two paragraphs,
complex numbers, imaginary numbers and pure
imaginary numbers, and their relationships to each
other and to real numbers.
Use the Developing Concepts Activity to introduce
Lesson 5.5. An alternative way to approach
Lesson 5.5 is to use the Application Lesson
Opener. Continue vocabulary file or algebra
glossary. Have students give an example of a
quadratic equation that can be solved using
completing the square with the coefficient of x2
being 1 and an example whose coefficient of x2 is
not 1; and then show how the method is used in
each problem. Have students do the Using
Technology Activity that uses a graphing
calculator to find maximum and minimum values
of quadratic functions.
Examples: 1-7,
pp. 272-276
Warm-Up Exercises: p. 53
WT: p. 35^
Lesson Opener (Activity):
p. 54
Checkpoint Exercises:
pp. 273-276
Practice A, B, & C:
pp. 55-57
HQ: p. 36^
Reteaching with Practice:
pp. 58-59
Quiz 2: p. 298, #’s 1-10
RS: Quiz 2: p. 91, #’s 1-4^
Perform operations with complex
numbers
Find the absolute value of complex
numbers
Chapter Reference 5.4
3.5 Solve quadratic equations
by completing the square:
Write quadratic functions in vertex
form.
Practice:
pp. 277-280,
#’s 17-114
(See Assignment
Guide, p. 277)
Interdisciplinary Application:
p. 61
Challenge: p. 62
Developing
Concepts: p. 281
(See p. 66 in RS)
Examples: 1-7,
pp. 282-285
Guided Practice:
p. 286, #’s 1-22
Practice:
pp. 286-289,
#’s 23-118
(See Assignment
Guide, p. 286)
Using Technology:
p. 290
Chapter Reference 5.5
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Guided Practice:
p. 277, #’s 1-16
Warm-Up Exercises: p. 65
WT: p. 36^
Lesson Opener (Application):
p. 67
Checkpoint Exercises:
pp. 283-285
Practice A, B, & C:
pp. 69-71
HQ: p. 37^
Reteaching with Practice:
pp. 72-73
Quiz 2: p. 298, #’s 11-17
RS: Quiz 2: p. 91, #’s 5-6^
Real Life Application: p. 75
Challenge: p. 76
Graphing Calculator Activity:
p. 68
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
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Learning Outcomes
Differentiated Instructional Activities
3.6 Solve quadratic equations
using the quadratic
formula.
An alternative way to approach Lesson 5.6 is to
use the Visual Approach Lesson Opener. Have
students copy the quadratic formula, and the
number and type of solutions of a quadratic
equation on 3X5 index cards. Continue vocabulary
file or algebra glossary. Remind students that they
can solve quadratic equations using factoring or by
completing the square, however; factoring cannot
be used for every quadratic equation while
completing the square can be a complicated
procedure. Writing Activity: Have students
explain the relationship between the discriminant
of a quadratic equation, the number and type of
solutions of the quadratic equation, and the
x-intercepts of its corresponding graph. Have
students do the graphing calculator activity.
Chapter Resource Book
References
Assessments#
Warm-Up Exercises:
p. 79
WT: p. 37^
Guided Practice:
p. 295, #’s 1-16
Lesson Opener (Visual
Approach): p. 80
Practice:
pp. 295-298,
#’s 17-102
(See Assignment
Guide, p. 295)
Practice A, B, & C:
pp. 83-85
Checkpoint Exercises:
pp. 292-294
HQ: p. 38^
Quiz 2: p. 298, #’s 18-22
RS: Quiz 2: p. 91, #’s 7-8^
Reteaching with Practice:
pp. 86-87
Interdisciplinary
Application: p. 89
Challenge: p. 90
Graphing Calculator
Activity: p. 81-82
Chapter Reference 5.6
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Text Book
References*
Examples: 1-5,
pp. 291-294
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet or appropriate Chapter Resource (RS) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
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