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The function given is \( P(x) = (x - 3)^2 (x - 9) \), and you are asked to find the \( y \)-intercept.

To find the \( y \)-intercept, we need to evaluate \( P(x) \) at \( x = 0 \), because the \( y \)-intercept occurs when \( x = 0 \).

### Steps:
1. Substitute \( x = 0 \) into the function:
   \[
   P(0) = (0 - 3)^2(0 - 9)
   \]
2. Simplify the terms:
   \[
   P(0) = (-3)^2 \cdot (-9)
   \]
   \[
   P(0) = 9 \cdot (-9)
   \]
   \[
   P(0) = -81
   \]

Thus, the \( y \)-intercept is \( y = -81 \).

Would you like further clarification or more details on this? Here are five related questions you might find useful:

1. How do you find the \( y \)-intercept for a general polynomial function?
2. What happens to the graph of \( P(x) \) around \( x = 3 \) since \( (x - 3)^2 \) is squared?
3. What are the roots of the given function, and how do they affect the graph?
4. How do you find the x-intercepts of the function \( P(x) \)?
5. What is the degree of the function, and how does it affect the end behavior?

**Tip**: For polynomials, the \( y \)-intercept is always found by evaluating the function at \( x = 0 \).

Given the function P(x) = (x - 3)^2(x - 9), find its y-intercept.

Learn how to find the y-intercept of the polynomial function P(x) = (x - 3)^2(x - 9). This problem illustrates key algebraic concepts, including evaluating a function at x = 0 and simplifying polynomial expressions. Suitable for students in Grades 9-12.

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