The given function is \( f(x) = 2(x - 6)^2 - 7 \). 

This is a quadratic function in vertex form, which is given by the equation:

\[
f(x) = a(x - h)^2 + k
\]

In this form, the vertex is \( (h, k) \), where:
- \( h \) is the x-coordinate of the vertex.
- \( k \) is the y-coordinate of the vertex.

By comparing \( f(x) = 2(x - 6)^2 - 7 \) with the vertex form, we can see that:
- \( h = 6 \)
- \( k = -7 \)

Thus, the vertex of the function is \( (6, -7) \).

Would you like further details or have any other questions?

Here are 5 related questions:
1. How do you find the vertex of a quadratic function in standard form?
2. What is the axis of symmetry for this function?
3. How does the value of \( a \) (in this case, 2) affect the shape of the parabola?
4. What are the x- and y-intercepts of this quadratic function?
5. How would you graph this quadratic function step-by-step?

**Tip:** The sign of \( a \) in the vertex form determines if the parabola opens upward (positive \( a \)) or downward (negative \( a \)).

Learn how to find the vertex of the quadratic function f(x)=2(x-6)^2-7. This problem covers key algebraic concepts such as vertex form, and provides a detailed explanation. Suitable for students in Grades 9-10.

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