To determine the coordinates of the vertex of the parabola from the graph, we observe the point where the parabola reaches its highest or lowest point. This vertex is a maximum in this case because the parabola opens downward (as it curves downward).

From the graph, we can see:

• The vertex occurs at $x = -6$, where the parabola reaches its highest point.
• The corresponding $y$-value is $y = 9$.

Thus, the coordinates of the vertex are $(-6, 9)$.

Would you like more details or have any questions?

Here are 5 related questions to further explore:

1. What is the equation of the parabola in vertex form given the vertex $(-6, 9)$?
2. How can we find the axis of symmetry for this parabola?
3. How can we determine the focus of the parabola from the graph?
4. How do you find the y-intercept and x-intercepts from the graph?
5. How can you verify if the parabola represents a quadratic function?

Tip: The vertex of a parabola provides critical information, including the maximum or minimum value of the function, and can be used to derive the equation of the quadratic.