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The function provided is \( g(x) = 3(x + 2)^2 - 6 \), and you are asked to find the vertex.

This function is in vertex form, which is \( g(x) = a(x - h)^2 + k \), where:
- \( (h, k) \) is the vertex.
- \( a \) determines the width and direction of the parabola.

From the equation \( g(x) = 3(x + 2)^2 - 6 \):
- The term \( (x + 2)^2 \) shows that \( h = -2 \) (since \( x + 2 \) can be written as \( x - (-2) \)).
- The constant \( -6 \) represents \( k \), so \( k = -6 \).

Therefore, the vertex is \( (-2, -6) \).

The correct answer is **\( (-2, -6) \)**.

Would you like any further details or clarifications?

Here are 5 follow-up questions related to this topic:
1. How does the value of \( a \) affect the shape of the parabola?
2. Can you find the axis of symmetry for this quadratic function?
3. What happens to the vertex if we change the equation to \( g(x) = 3(x - 2)^2 - 6 \)?
4. How do you find the x-intercepts of this quadratic function?
5. What is the y-intercept of the given quadratic function?

**Tip**: The vertex form of a quadratic function directly reveals the vertex, making it easy to identify key properties like the maximum or minimum point!

Which is the vertex of the quadratic function g(x) = 3(x + 2)^2 - 6?

Learn how to find the vertex of the quadratic function g(x) = 3(x + 2)^2 - 6. This problem demonstrates the use of the vertex form of a quadratic equation to easily identify the vertex. Suitable for students in Grades 9-11.

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