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

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.