The graph you provided represents a downward-opening parabola.

Domain:

The domain of a function is the set of all possible $x$-values that the function can take. Since the parabola extends indefinitely in both the left and right directions (as shown by the arrows), the domain is all real numbers. In interval notation, the domain is: $(-\infty, \infty)$

Range:

The range of a function is the set of all possible $y$-values that the function can take. The parabola reaches a maximum at $y = 6$ (the vertex), and it decreases as you move away from this point in both directions. The graph doesn't go above $y = 6$ but extends downward indefinitely, so the range is: $(-\infty, 6]$

Summary:

• Domain: $(-\infty, \infty)$
• Range: $(-\infty, 6]$

Would you like more details, or do you have any other questions?

Here are 5 related questions:

1. How do you find the vertex of a parabola from a graph?
2. What is the general form of a quadratic function, and how does it relate to its graph?
3. How does the direction of the parabola change when the coefficient of $x^2$ changes?
4. What are other ways to determine the range of a quadratic function besides using a graph?
5. How does the vertex form of a quadratic equation help in graphing?

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