https://file.aiquickdraw.com/mathbot/file/1727572734206dzmz60xr.jpg

Let's analyze the graph and the questions step by step:

1. **Graph Behavior**:
   The parabola in the image opens **upward**. This is evident because the arms of the parabola extend upward as \( x \) moves away from the vertex. When a parabola opens up, it has a **minimum** point at its vertex, as it is the lowest point on the graph.

   - Answer: **opens up, minimum**

2. **Vertex**:
   The vertex is the lowest point of the parabola, and based on the graph, the vertex appears to be at \( (-1, -8) \).

   - Answer: **(-1, -8)**

3. **Y-Intercept**:
   The y-intercept occurs where the parabola crosses the y-axis. This happens when \( x = 0 \), and based on the graph, the parabola crosses the y-axis at \( y = -7 \).

   - Answer: \( (0, -7) \)

4. **X-Intercepts**:
   The x-intercepts are the points where the parabola crosses the x-axis. Based on the graph, the parabola crosses the x-axis at \( x = -3 \) and \( x = 1 \).

   - Answer: **x = -3, 1**

### Summary of Answers:
- **Graph behavior**: Opens up, minimum.
- **Vertex**: \( (-1, -8) \).
- **Y-Intercept**: \( (0, -7) \).
- **X-Intercepts**: \( x = -3, 1 \).

Do you have any questions or need further details? Here are some related questions for practice:

1. How do you find the vertex of a parabola from its equation in vertex form?
2. What is the significance of the sign of the coefficient of \( x^2 \) in a parabola's equation?
3. How can you algebraically determine the y-intercept from a quadratic equation?
4. How does changing the value of the y-intercept affect the graph of a parabola?
5. How do you factor a quadratic equation to find its x-intercepts?

**Tip**: To quickly identify the direction a parabola opens, check the sign of the coefficient of the \( x^2 \) term in its equation—positive means it opens up, and negative means it opens down.

Does the graph open up or down? Does the graph have a maximum or a minimum? The vertex is (___, ___). The y-intercept is (0, ___). Find the two values of x that correspond to the x-intercepts of the parabola and write them as a list, separated by commas: x = ___

This math problem focuses on analyzing the graph of a parabola. The question explores determining the direction of the parabola (whether it opens up or down), finding the vertex, identifying the y-intercept, and solving for the x-intercepts. A comprehensive explanation of quadratic functions and their key properties is included, suitable for students in Grades 8-10.

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