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Mat 0104 Intermediate Algebra
Review of Module 12 Objectives: Mastering Complex Numbers and Quadratics
12.1 – Definition of i, definition of a complex number, operations on complex
numbers that include simplifying a complex number, addition, subtraction,
multiplication and division.
1. Using the definition of ‘i’, simplify √-9.
2. Identify the real and imaginary components of the complex number 7 – 6i.
3. Simplify each:
a. Add- (9 – 5i) + (8 + 3i)
b. Subtract- (-8 + 6i) - (7 + 3i)
c. Multiply- (2 –i)(2 + i)
d. Divide-
12.2 – Solve a quadratic equation by Factoring, using the Square Root Method,
Completing the Square Method, Using the Quadratic Formula.
1. Solve the quadratic equation by factoring.
x2 – 3x -18 = 0
2. Solve the quadratic equation using the square root property. (x – 3)2 = 16
3. Solve the quadratic equation using completing the square method. x2 + 12x = 18
4. Solve the quadratic equation using the quadratic formula. 2x2– 3x - 5 = 0
Module 12 Objectives: Mat 0104 Mastering Complex Numbers and Quadratics
12.3 – Solving Equations that are Reducible to Quadratic Equations (substitution
method).
Solve the following quadratic equation using “u” substitution. x4 - x2- 6 = 0
12.4 – Applications of Quadratic Equations and properties of and graph a parabola.
1. The length of a rectangle is five more than its width. If the area of the
rectangle is 24 cm, what are the dimensions of the rectangle?
2. Graph the following:
a. f(x) = x2
b. f(x) = 4x2
c. How do the graphs differ? How are they the same?
3. Graph the following:
a. f(x) = x2
b. f(x) =
c. How do the graphs differ? How are they the same?
4. Graph the following:
a. f(x) = x2
b. f(x) = -x2
c. How do the graphs differ? How are they the same?
Review of Module 12 Objectives: Mat 0104
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Module 12 Objectives: Mat 0104 Mastering Complex Numbers and Quadratics
5. Graph the following:
a. f(x) = x2
b. f(x) = x2 + 5
c. How do the graphs differ? How are they the same?
6. Graph the following:
a. f(x) = x2
b. f(x) = x2 - 6
c. How do the graphs differ? How are they the same?
7. Graph the following:
a. f(x) = x2
b. f(x) =(x - 3)2
c. How do the graphs differ? How are they the same?
8. Graph the following:
a. f(x) = x2
b. f(x) = (x + 4)2
c. How do the graphs differ? How are they the same?
Review of Module 12 Objectives: Mat 0104
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