To analyze the graphs and determine the number of imaginary zeros for the functions:

Exercise 9 (Degree: 5)

• Graph Behavior: The polynomial is of odd degree (5), which means it starts and ends in opposite directions. The graph crosses the x-axis three times.
• Real Zeros: There are 3 real zeros.
• Imaginary Zeros: The total number of zeros must equal the degree of the polynomial. Since 3 are real, the remaining $5 - 3 = 2$ zeros are imaginary.

Exercise 10 (Degree: 4)

• Graph Behavior: The polynomial is of even degree (4), which means it starts and ends in the same direction. The graph crosses the x-axis two times.
• Real Zeros: There are 2 real zeros.
• Imaginary Zeros: The total number of zeros must equal the degree of the polynomial. Since 2 are real, the remaining $4 - 2 = 2$ zeros are imaginary.

Explanation of Imaginary Zeros

Imaginary zeros always occur in conjugate pairs (e.g., $a + bi$ and $a - bi$), which explains why both graphs have an even number of imaginary zeros.

Would you like further clarification on polynomial zeros, graph analysis, or related topics?

Here are 5 questions to deepen your understanding:

1. How can you determine the degree of a polynomial based on its end behavior?
2. Why do imaginary zeros of polynomials occur in conjugate pairs?
3. Can a polynomial have more imaginary zeros than its degree?
4. What is the significance of the x-axis crossings in finding real zeros?
5. How does the Fundamental Theorem of Algebra relate to this problem?

Tip: Remember, the number of real zeros is equal to the number of x-intercepts on the graph, while imaginary zeros do not appear visually on the graph.