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 $x = 0$.