https://file.aiquickdraw.com/mathbot/file/17288446205608f96u4ju.jpg

To find the vertex of the function \( g(x) \) in question #13, let's first analyze the table of values for \( g(x) \):

| \( x \) | \( g(x) \) |
|--------|------------|
| -2     | -6         |
| -1     | -3         |
| 0      | 0          |
| 1      | -3         |
| 2      | -6         |

The function \( g(x) \) seems to follow a quadratic pattern since the values of \( g(x) \) decrease, reach a minimum, and then increase symmetrically.

### Symmetry in Quadratic Functions
The vertex of a quadratic function is where the function reaches its maximum or minimum point. In this case, the function decreases until \( x = 0 \), where \( g(x) = 0 \), and then increases symmetrically afterward.

### Finding the Vertex
The vertex of a parabola is the point where the function changes direction. Here, based on the symmetry in the table, the vertex occurs at \( x = 0 \), and the corresponding \( g(x) = 0 \).

Thus, the vertex is:
\[
(0, 0)
\]

Would you like to explore further details or have any questions on this?

### Related Questions:
1. What is the general form of a quadratic function?
2. How can you derive the vertex from a quadratic equation in standard form?
3. What is the axis of symmetry for the quadratic function \( g(x) \)?
4. Can we use other methods (e.g., completing the square) to confirm the vertex?
5. How would we find the vertex if the quadratic equation were not symmetric?

#### Tip:
The vertex formula for a quadratic function in the form \( ax^2 + bx + c \) is \( x = -\frac{b}{2a} \). Keep this in mind when solving equations without symmetry in the table.

Learn how to find the vertex of the quadratic function g(x) using a table of values. This problem focuses on identifying the symmetry of the function and determining the vertex point, suitable for students in Grades 8-10.

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