The graph you uploaded shows a parabolic curve, which is symmetric about the y-axis and opens downward.

Domain:

The domain of a function refers to all the possible values of $x$ for which the function is defined. In this case, the parabola extends infinitely to the left and right along the x-axis, meaning the function is defined for all real numbers.

• Domain: $(-\infty, \infty)$

Range:

The range refers to all the possible values of $y$ that the function can take. Since the parabola opens downward, it has a maximum value at the vertex, and the graph extends downwards infinitely. The highest point on the graph (the vertex) appears to be at $y = 0$, and it decreases without bound.

• Range: $(-\infty, 0]$

Final Answer:

• Domain: $(-\infty, \infty)$
• Range: $(-\infty, 0]$

Do you want more details or explanations on this?

Here are five questions to consider:

1. How do you find the vertex of a parabola algebraically?
2. What would change about the domain and range if the parabola opened upwards?
3. How would you express the domain and range in set-builder notation?
4. How do transformations (translations, reflections) affect the domain and range of parabolas?
5. How can you determine the equation of the parabola from the graph?

Tip: The domain of most parabolas is all real numbers unless there are specific restrictions (like a real-world scenario limiting $x$).