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The given function is:

\[
f(x) = -6(x - 7)(x + 11)
\]

This is a quadratic function in factored form. To find the x-coordinate of the vertex, we can use the property that the vertex lies exactly midway between the two roots of the quadratic function.

### Step-by-Step Solution:

1. **Find the roots of the quadratic**:
   - From the factor \((x - 7)\), the first root is \(x = 7\).
   - From the factor \((x + 11)\), the second root is \(x = -11\).

2. **Find the midpoint** (x-coordinate of the vertex):
   The midpoint between the two roots is the average of 7 and -11:
   
   \[
   x_{\text{vertex}} = \frac{7 + (-11)}{2} = \frac{-4}{2} = -2
   \]

Thus, the x-coordinate of the vertex is \(x = -2\).

Would you like further details or clarifications?

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Here are 5 related questions to explore further:

1. What is the y-coordinate of the vertex for this quadratic function?
2. How do you convert a quadratic equation from factored form to standard form?
3. What are the roots of the quadratic function, and how are they related to the graph?
4. How does the value of the coefficient (-6) affect the direction of the parabola?
5. What is the axis of symmetry of this quadratic function?

**Tip**: The vertex form of a quadratic function is often helpful for quickly identifying the vertex and graphing the parabola.

Given: f(x) = -6(x - 7)(x + 11), Find the x-coordinate of the vertex.

Learn how to find the x-coordinate of the vertex for the quadratic equation f(x) = -6(x - 7)(x + 11). This solution explains key concepts like factored form, quadratic equations, and the midpoint formula. Suitable for students in Grades 9-10.

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