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.