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 $x = 0$.