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The given function is \( f(x) = 6(x - 9)^2 + 11 \).

This is a quadratic function in vertex form, which is generally expressed as:
\[
f(x) = a(x - h)^2 + k
\]
Where:
- \( (h, k) \) is the vertex of the parabola.
- \( a \) is a coefficient that affects the direction and width of the parabola.

For the function \( f(x) = 6(x - 9)^2 + 11 \):
- The vertex is at \( (h, k) \), where \( h = 9 \) and \( k = 11 \).

Thus, the vertex of the function is \( (9, 11) \).

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:
1. How does changing the value of \( a \) affect the graph of a quadratic function?
2. What is the axis of symmetry for this quadratic function?
3. How can you convert a quadratic function from standard form to vertex form?
4. How do you determine whether a parabola opens upwards or downwards?
5. How does the vertex form help in finding the maximum or minimum value of a quadratic function?

**Tip:** The sign of \( a \) (here 6) tells you if the parabola opens upwards (positive \( a \)) or downwards (negative \( a \)).

Find the vertex of the quadratic function f(x) = 6(x - 9)^2 + 11.

Learn how to find the vertex of the quadratic function f(x) = 6(x - 9)^2 + 11. This step-by-step guide covers key concepts from algebra, including the vertex form and the role of coefficients in determining the shape of the parabola. Suitable for students in Grades 8-10.

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