what is the y intercept of f(x)=(x-8)(x+5)(x-6)^2

To find the y-intercept of the function \( f(x) = (x - 8)(x + 5)(x - 6)^2 \), we substitute \( x = 0 \) into the equation, since the y-intercept occurs where \( x = 0 \).

### Step-by-Step Solution:

1. Substitute \( x = 0 \) into \( f(x) \):
   \[
   f(0) = (0 - 8)(0 + 5)(0 - 6)^2
   \]

2. Simplify each term:
   - \( 0 - 8 = -8 \)
   - \( 0 + 5 = 5 \)
   - \( 0 - 6 = -6 \) and \( (-6)^2 = 36 \)

3. Now, multiply these results:
   \[
   f(0) = (-8)(5)(36)
   \]

4. Calculate \( (-8) \times 5 = -40 \) and then \( -40 \times 36 = -1440 \).

Therefore, the y-intercept of the function is:
\[
\boxed{-1440}
\]

Would you like further details on any part of the process?

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Here are 5 related questions for further practice:

1. What is the y-intercept of \( g(x) = (x + 3)(x - 4)^2(x + 2) \)?
2. How do you find the y-intercept of a polynomial function generally?
3. What are the x-intercepts of \( f(x) = (x - 8)(x + 5)(x - 6)^2 \)?
4. How would the y-intercept change if the function had an additional constant factor?
5. Can a polynomial function have more than one y-intercept?

**Tip:** To find the y-intercept of any function, substitute \( x = 0 \) and simplify the result.

What is the y intercept of f(x)=(x-8)(x+5)(x-6)^2

Learn how to find the y-intercept of the polynomial function f(x) = (x - 8)(x + 5)(x - 6)^2 by substituting x = 0 and simplifying. This problem covers key concepts in polynomial functions and intercept calculations, making it suitable for students in Grades 9-11.

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