Algebra II Unit #3: Quadratic Functions and Factoring
Essential Questions:
1) How can I graph and write quadratic functions in several forms?
2) How can I solve quadratic equations using a variety of methods?
3) How do I perform operations with square roots and complex numbers?
Book Journal Questions:
p274 #1&4, p282 #75,
p298 #70, p316 #7
EC: p274 #3, p299 #73
Vocab: quadratic function
vertex
the imaginary unit (i)
root/zero of an equation
zero product property
imaginary numbers
axis of symmetry
radical/radicand
complex number
completing the square
difference of squares
perfect square trinomial
quadratic formula
vertex form
conjugates
parabola
rationalizing the denominator
discriminant
Khan Academy Sections: Test #1 Graphing parabolas in standard form, graphing parabolas in vertex form, vertex
of a parabola, factoring quadratics 2, factoring difference of squares 2, solving quadratics by factoring 2, solving
quadratics by taking the square root. Test #2 Adding and subtracting complex numbers, multiplying complex
numbers, dividing complex numbers, solving quadratics by completing the square 1, using the quadratic formula,
solutions to quadratic equations.
Homework Check
5 points
4 points
Algebra II Section/Lesson
Assigned Problems
3 points
Day 1
Pre-Test/Word Walls/Journal Questions
Day 2
4.1 Graphing Quadratic Functions in
Standard Form (#1)
*How can one find the max/min of a
quadratic function in standard form?
Day 3
4.1 Graphing Quadratic Functions in
Standard Form (#2)
*How do we graph quadratic equations
in standard form?
Day 4
4.2 Graphing Quadratic Functions in
Vertex Form (#1)
Word Wall/Pre-Test/
Prerequisite Skills
Pages 240-243
(17)
x: 1, 2, 4, 6, 34-37,41,
42, 58, 66, 67, 71-74
(20)
y: 1, 2, 3-6, 33-36, 41,
42, 57, 63-65, 69-71, 74
Pages 240-243
JQ: p274 #1
(8)
x: 11, 14, 17, 25-28, 48
(11)
y: 11-15, 24, 25, 27, 4446, 48
(11)
(13)
Pages 249-251
x: 6-10, 43, 45, 59-62
y: 4-11, 59-63
*How do we graph quadratic equations
in vertex form?
Day 5
4.2 Graphing Quadratic Functions in
Vertex Form (#2)
*How do I find the max/min value of a
quadratic function?
(12)
66-69
(13)
69
Pages 249-251
x: 28-30, 38-40, 52, 53,
y: 25-28, 35-38, 51, 66-
Day 6
No Stamp Needed
Quiz Lessons 4.1-4.2
Work on journal questions
4.3 Solve x2 + bx + c =0 by Factoring
Day 7
*How can I factor quadratics when the
leading coefficient is 1?
4.4 Solve ax2 + bx + c =0 by Factoring
(#1)
Day 8
*How can I factor quadratics when the
leading coefficient is not 1?
4.4 Solve ax2 + bx + c =0 by Factoring
(#2)
Day 9
* How can I factor quadratics when the
leading coefficient is not 1?
Day 10
Pages 255-258
(18)
x: 10, 11, 14, 16-18, 3134, 60, 78-80, 83, 85, 87, 90
(22)
y: 6, 8, 9, 15, 16, 18, 19,
26-32, 59, 77-80, 83, 85, 87
Pages 263-265
(15)
x: 7, 8, 10, 14, 17, 20,
32, 37-39, 69-72, 75
(17)
y: 4-8, 13, 16, 19, 32,
36, 37, 39, 69-72, 75
Pages 263-265
JQ: p274 #4
(14)
x: 24-28, 34, 40, 52, 5456, 60, 78, 80
(15)
y: 22-25, 27, 28, 33-35,
51, 53, 54, 57, 78, 80
4.5 Solve Quadratic Equations by
Finding Square Roots (#1)
*How do I simplify radical expressions?
Day 11
4.5 Solve Quadratic Equations by
Finding Square Roots (#2)
Pages 269-271
(23)
Everyone: 3-17, 20, 4649, 54, 56, 59
(13)
(14)
Pages 269-271
x: 25-33, 34, 39, 60, 61
y: 23-33, 39, 60, 61
*How can you use square roots to solve
a quadratic equation?
Day 12
No Stamp Needed
Quiz Lessons 4.3-4.5
Work on journal questions
No Stamp Needed
Review Day
Study for test
Day 13
Day 14
No Stamp Needed
Unit 3 Test (Part 1, 4.1-4.5)
Work on journal questions
Day 15
4.6 Perform Operations with Complex
Numbers (#1)
*How do you perform operations on
complex numbers?
Day 16
4.6 Perform Operations with Complex
Numbers (#2)
* How do you perform operations on
complex numbers?
Day 17
(21)
86-88
(24)
Day 18
(18)
81-83
(21)
83
4.7 Completing the Square (#2)
*How can I convert quadratic equations
in standard form to vertex form?
y: 3-21, 79, 80, 86-88
Pages 279-282
JQ: p282 #75
(20)
x: 23-33, 52, 53, 56, 59,
66, 67, 82-84
(22)
y: 22-33, 51-53, 57, 60,
65, 66, 82-84
4.7 Completing the Square (#1)
*How is the process of completing the
square used to solve quadratic
equations?
Pages 279-282
x: 4-11, 13-20, 79, 80,
(12)
76-78
(13)
78
Pages 288-291
x: 5-10, 17-20, 23-27,
y: 3-8, 13-18, 22-27, 81-
Pages 288-291
x: 29-32, 36, 37, 43-45,
y: 28-33, 35, 42-44, 76-
Day 19
No Stamp Needed
Day 20
Quiz Lessons 4.6-4.7
4.8 Use the Quadratic Formula and
Discriminant (#1)
*How do you use the quadratic
formula?
Day 21
4.8 Use the Quadratic Formula and
Discriminant (#2)
*What does the discriminant tell you
about a quadratic equation?
Work on journal questions
(17)
79, 87
(19)
79, 87
Pages 296-299
x: 4-9, 14, 17-20, 50, 76y: 3-10, 13-17, 49, 76-
Pages 296-299
JQ: p298 #70
(12)
x: 31, 36, 37, 42, 43, 45,
52-54, 81-83
(13)
y: 31-33, 38, 40-42, 5254, 81-83
JQ: p316 #7
Day 22
No Stamp Needed
Review Day
Study for test
Day 23
Journal Question Work Day
No Stamp Needed
*How can different problem solving
strategies be used to solve word
problems?
No Stamp Needed
Unit 3 Test
(Part 2, mainly 4.6-4.8)
Work on journal questions or
review for the test
Day 24
Finish journal questions!
Journal Questions
Book Problems:
p274 #1&4, p282 #75, p298 #70, p316 #7
Extra Credit:
p274 #3, p299 #73
ACT Prep: (Only 0.5 pts given for correct answer. The only 1.5 pts must come from sufficient and correct work shown)
1) Which of the following statements is NOT true about the parabola seen below?
(A)
The x-intercepts are -2 and 4.
(B)
The y-intercept is between 2 and 3.
(C)
The minimum value is 3.
(D)
The axis of symmetry is x = 1.
(E)
The vertex is (1, 3).
2) What is the equation of the parabola seen above?
1
2
8
(A)
𝑦 = 𝑥 2 + 2𝑥 − 8
(B)
𝑦 = − 3 𝑥2 + 3 𝑥 + 3
(C)
𝑦 = −𝑥 2 + 2𝑥 + 8
1
8
𝑦 = − 𝑥 2 − 2𝑥 −
(D)
𝑦 = −3𝑥 2 + 6𝑥 + 24
(E)
3
3
3) If the parabola 2𝑥 2 + 𝑏𝑥 + 4 passes through the
point (2, 24) then the value of b must be:
(A)
5
(B)
6
(C)
9
(D)
18
(E)
36
4) The value of 𝑖 21 is:
(A)
-1
(B)
1
(C)
𝑖
(D)
−𝑖
(E)
None of these
5) The diagram below shows a circle inscribed in a square. The area of the shaded region is 21.5 in2. To the
nearest tenth of an inch, how long is the radius of the circle?
(A)
(B)
(C)
(D)
(E)
2.3 in
4.4 in
4.8 in
5.0 in
6.2 in