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To find the **y-intercept** of the polynomial function, we need to evaluate \( f(x) \) at \( x = 0 \).

The given polynomial function is:

\[
f(x) = 2x - x^4 - 7x^2 + 6x^3
\]

Substitute \( x = 0 \) into this equation:

\[
f(0) = 2(0) - (0)^4 - 7(0)^2 + 6(0)^3
\]

Simplifying:

\[
f(0) = 0 - 0 - 0 + 0 = 0
\]

Thus, the **y-intercept** is \( 0 \).

Let me know if you'd like more details or have any questions! Here are some related questions to deepen understanding:

1. How do you find the y-intercept of any polynomial function?
2. What is the significance of the y-intercept in graphing?
3. How can you find the x-intercepts of this polynomial?
4. What would the graph of this polynomial roughly look like?
5. How do higher-degree terms (like \(x^4\)) affect the graph?

**Tip**: The y-intercept is always found by setting \( x = 0 \) and solving for \( y \).

Find the y-coordinate of the y-intercept of the polynomial function: f(x) = 2x - x^4 - 7x^2 + 6x^3

Learn how to find the y-intercept of a polynomial function, f(x) = 2x - x^4 - 7x^2 + 6x^3, by substituting x = 0 and evaluating the equation. This problem helps in understanding intercepts and polynomial behavior. Suitable for Grades 9-12.

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