Graph Interpretation:

The graph depicts a parabola that opens upwards. Here’s a breakdown:

1. Vertex: The lowest point on the parabola appears to be at $(1, -3)$.

2. Domain: Since the parabola extends infinitely to the left and right, the domain is all real numbers. In interval notation, this is written as: $\text{Domain}: (-\infty, \infty)$

3. Range: The range of the function is determined by the $y$-values that the parabola attains. Since the vertex is the minimum point, and the parabola opens upwards, the range starts at $y = -3$ and extends to positive infinity. In interval notation, the range is: $\text{Range}: [-3, \infty)$

Final Answer:

• Domain: $(-\infty, \infty)$
• Range: $[-3, \infty)$

Would you like to explore any specific details further or need clarification on any part of this explanation?

Follow-up Questions:

1. How would you write the equation of this parabola given the vertex and a point on the graph?
2. What happens to the domain and range if the parabola opens downwards?
3. Can you determine the axis of symmetry for this parabola?
4. What are the possible x-intercepts of this parabola?
5. How does changing the vertex affect the domain and range of the function?

Tip:

When identifying the range of a parabola, always consider the direction in which it opens (upwards or downwards) and the $y$-coordinate of the vertex.