Name: ________________________________________ Date: _______________________ Period: ________
Unit 1 Homework Packet – Quadratic Functions
1.1 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
1.2 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
1.2 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
1.3 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
1.4 Complex Numbers
Directions – Par 1. Evaluate each of the following complex roots.
1.
−64
3.
−144
5.
−32
2.
−100
4.
−50
6.
16 + −4
Directions – Part 2. Perform each of the following operations and simplify your answer.
7.
8.
9.
(5 + 3i) + (6 – 2i)
(3 – 2i) – (4 – 5i)
(4 + 5i)(3 – 2i)
10. (7 + 6i)(3 – 5i)
13.
7−4𝑖
2+𝑖
14.
1−𝑖
1+𝑖
11. – 2i(6 – 4i)
12. (6 –
2i)2
Directions – Part 3. Solve each of the following quadratic equations that have complex
roots. (The solutions are Complex numbers instead of Real)
15. x2 + 25 = 0
17. 9x2 + 100 = 0
19. x2 + 8 = 0
16. 4x2 + 16 = 0
18. 121x2 + 144 = 0
20. 3x2 + 9 = 0
1.5 The Quadratic Formula
Directions. Solve using the quadratic formula. You must show your work on a separate
page.
2
𝑥=
−𝑏 ± 𝑏 − 4𝑎𝑐
2𝑎
1. x2 – 5x – 14 = 0
2. x2 + 3x – 2 = 0
3. x2 +10x + 22 = 0
4. -x2 + 7x – 19 = 0
5. 5x2 + 3x – 1 = 0
6. 3x2 – 11x – 4 = 0
7. 3x2 + 6x = -2
8. 8x2 – 8x = 1
9. 5x2 + 9x = -x2 + 5x + 1
1.6 Completing the Square
Directions – Part 1. Solve by completing the square.
1. x2 + 2x = 9
2. x2 – 12x = -28
3. x2 + 20x + 104 = 0
4. x2 – 4x = 2x + 35
5. 2x2 – 12x = -14
6. -3x2 + 24x = 27
Directions – Part 2. Rewrite each quadratic function in vertex form.
7. y = x2 – 6x + 11
8. y = x2 – 2x – 9
9. y = x2 + 16x + 14
Directions – Part 3. Use area formulas to find the value of x.
10. Area of rectangle = 100
11. Area of triangle = 40
12. Area of trapezoid = 70
13. Area of parallelogram = 54