1. Quadratic Functions and Equations
Chapter 3
Quadratic Functions and Equations

2. Complex Numbers 3.3 Perform arithmetic operations on complex numbers
Solve quadratic equations having complex solutions

3. Teaching Example 1
Simplify each expression.
Solution

4. Teaching Example 2
Simplify each expression.
Solution

5. Teaching Example 3
Write each expression in standard form.
Solution

6. Teaching Example 3 (continued)
Multiply by
Expand.
i2 = −1
Simplify.

7. Teaching Example 4
Simplify each power of i. a. i15 b. i10
Solution

8. Teaching Example 5
Solve each quadratic equation. Support your results graphically.

9. Teaching Example 5 (continued)
a = 1, b = 4, c = 5

10. Teaching Example 5 (continued)
The graph of does not intersect the x-axis, which indicates that the equation has no real solutions.

11. Teaching Example 5 (continued)
Solution
(b)
a = 2, b = −3, c = 5

12. Teaching Example 5 (cont)y1 y2
The graphs of and do not intersect, which indicates that the equation has no real solutions.

13. Teaching Example 5 (continued)
a = −4, b = 0, c = −3

14. Teaching Example 5 (continued)y2 y1
The graphs of and do not intersect, which indicates that the equation has no real solutions.