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To find the **y-coordinate** of the **y-intercept** of the function \( f(x) = (x^2 + 4)(x - 2) \), we follow these steps:

### Step 1: Identify the y-intercept
The **y-intercept** occurs where \( x = 0 \). Therefore, substitute \( x = 0 \) into the function to find \( f(0) \).

### Step 2: Calculate \( f(0) \)

\[
f(0) = (0^2 + 4)(0 - 2)
\]
\[
f(0) = (0 + 4)(-2)
\]
\[
f(0) = 4 \times (-2) = -8
\]

### Conclusion:
The **y-coordinate** of the y-intercept is \( -8 \).

Would you like more details or have any further questions? Here are some related questions for further exploration:

1. How do you find the x-intercepts of the polynomial function?
2. What are the roots of \( f(x) = (x^2 + 4)(x - 2) \)?
3. How does the degree of the polynomial affect its graph?
4. What is the significance of the complex roots of \( x^2 + 4 = 0 \)?
5. How do you expand the given polynomial?

**Tip:** The y-intercept is always where the function intersects the y-axis, and it occurs when \( x = 0 \).

Find the y-coordinate of the y-intercept of the polynomial function defined as f(x) = (x^2 + 4)(x - 2).

Discover how to find the y-intercept of the polynomial function f(x) = (x^2 + 4)(x - 2). This problem involves fundamental algebraic concepts and is suitable for students in Grades 9-11.

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