Name: ________________________________________ Date: _______________________ Period: ________
Unit 7 Homework Packet – Quadratic Functions
7.1 Introduction to Quadratic Functions
Directions. Factor the following quadratic expressions using the “Trident Method” or say
if they cannot be factored.
1. 20x2 + 50x – 120
2. 3x2 + 12x – 15
3. 18x2 + 15x + 3
4. 2x2 – x – 15
5. 5x2 + 4x – 3
6. 2x2 – 11x – 21
7. 2x2 – 12x - 54
8. 4x2 + 36x + 80
9. 5x2 + 5x – 60
10. 6x3 + 12x2 + 12x
11. 4x2 + 16x + 16
12. 10x4 + 10x3 – 120x2
7.2 Factoring Quadratic Binomials
Directions. Factor the following quadratic expressions using “Difference of Squares” or
by dividing out the GCF.
1. 9x2 + 18x
2. 12x2 – 4x
3. 15x3 – 3x2
4. 20x4 + 15x3
5. 18x2 – 16x
6. 25x2 – 100
7.2 Factoring Quadratic Binomials – Continued
Directions. Continue Factoring the following quadratic expressions using “Difference of
Squares” or by dividing out the GCF.
7. 45x2 – 80
8. x2 – 16
9. 4x2 – 16
10. 16x2 – 1
11. 9x2 – 4y2
12. 25x2 – 3
13. x2 – 25y2
14. x2 – 2
15. 5x2 – 4
7.3 The Zero-Product Property
Directions. Solve the following quadratic equations by factoring and then applying the
Zero-Product Property
1. 3x2 – 5x – 2 = 0
2. 2x2 + 2x – 60 = 0
3. x2 – 25 = 0
4. 12x2 + 5 = 19x
5. 3x2 + 14x = 24
6. 9x2 – 81x = 0
7. 5x2 + 30x = 35
8. 25x2 – 100 = 0
9. 2x2 = 9x + 5
10. x2 – 3 = 0
11. 7x = - 14x2
12. 30x2 + 10x – 100 = 0
7.4 Complex Numbers & The Quadratic Formula
Directions – Part 1. Evaluate each of the following complex roots.
1.
−64
3.
−144
5.
−32
2.
−100
4.
−50
6.
16 + −4
Directions – Part 2. Solve using the quadratic formula. You must show your work on a
separate page.
2
𝑥=
−𝑏 ± 𝑏 − 4𝑎𝑐
2𝑎
7. x2 – 5x – 14 = 0
8. x2 + 3x – 2 = 0
9. x2 +10x + 22 = 0
10. -x2 + 7x – 19 = 0
11. 5x2 + 3x – 1 = 0
12. 3x2 – 11x – 4 = 0
13. 3x2 + 6x = -2
14. 8x2 – 8x = 1
15. 5x2 + 9x = -x2 + 5x + 1
7.5 Graphing Standard Form
Directions. For each of the following:
a) Find the axis of symmetry
b) Find the vertex
c) Create a table of values
d) Graph the function on the coordinate plane provided
e) State the Domain and Range
1
1. 𝑦 = 𝑥2 – 2𝑥 + 3
2. 𝑦 = 2 𝑥2 – 4𝑥 + 3
a) Axis of Symmetry: _________
b) Vertex: ____________
a) Axis of Symmetry: _________
b) Vertex: ____________
x
y
e) Domain and Range: __________
e) Domain and Range: __________
3. 𝑦 = −𝑥2 + 6𝑥 − 8
4. 𝑦 = 𝑥2 − 𝑥 + 2
a) Axis of Symmetry: _________
b) Vertex: ____________
y
x
y
a) Axis of Symmetry: _________
b) Vertex: ____________
x
e) Domain and Range: __________
x
y
e) Domain and Range: __________
7.5 Graphing Standard Form - Continued
Directions. For each of the following:
a) Find the axis of symmetry
b) Find the vertex
c) Create a table of values
d) Graph the function on the coordinate plane provided
e) State the Domain and Range
5. 𝑦 = −2𝑥2 – 8𝑥 − 4
6. 𝑦 = 𝑥2 – 5
a) Axis of Symmetry: _________
b) Vertex: ____________
a) Axis of Symmetry: _________
b) Vertex: ____________
x
y
e) Domain and Range: __________
e) Domain and Range: __________
7. 𝑦 = −𝑥2 + 3
8. 𝑦 = 2 𝑥2 + 2𝑥 + 2
y
x
y
1
a) Axis of Symmetry: _________
b) Vertex: ____________
a) Axis of Symmetry: _________
b) Vertex: ____________
x
e) Domain and Range: __________
x
y
e) Domain and Range: __________