The image shows a graph of a quadratic function and a question asking to determine the domain of the function.

Analyzing the Graph:

The function displayed is a parabola, which opens downward. The equation provided in the problem is $f(x) = -x^2 + 12x - 10$.

Domain of the Function:

For any quadratic function $f(x) = ax^2 + bx + c$, the domain is all real numbers because there are no restrictions on the values $x$ can take. This is true for the given function $f(x) = -x^2 + 12x - 10$ as well.

Thus, the domain of the function is: $(-\infty, \infty)$

Would you like a detailed explanation of how I derived this, or do you have any specific questions?

Here are some related questions that expand on this topic:

1. What is the range of the quadratic function $f(x) = -x^2 + 12x - 10$?
2. How do you find the vertex of the quadratic function $f(x) = -x^2 + 12x - 10$?
3. What are the zeros (roots) of the quadratic function $f(x) = -x^2 + 12x - 10$?
4. How can you determine if a quadratic function opens upward or downward?
5. How do you convert the quadratic function from standard form to vertex form?

Tip: For any quadratic function $ax^2 + bx + c$, if $a > 0$, the parabola opens upward; if $a < 0$, it opens downward.