https://file.aiquickdraw.com/mathbot/file/1726757700274t1fs70e6.jpg

Let's analyze the graph and fill in the table based on the information from the image.

1. **(a) Parabola's Direction:**
   The parabola opens **downward** because the arms of the curve are pointing down.

2. **(b) Vertex Coordinates:**
   The vertex is the highest point of the parabola, located at the coordinates **(0, 4)**.

3. **(c) Axis of Symmetry:**
   The axis of symmetry is a vertical line that passes through the vertex. Since the x-coordinate of the vertex is 0, the equation of the axis of symmetry is **x = 0**.

4. **(d) Intercepts:**
   - **x-intercepts:** The parabola crosses the x-axis at two points. From the graph, these x-intercepts appear to be **(-2, 0)** and **(2, 0)**.
   - **y-intercept:** The y-intercept is where the parabola crosses the y-axis, which occurs at **(0, 4)**.

Here is the filled table:
- **(a)** Downward
- **(b) Vertex:** (0, 4)
- **(c) Axis of symmetry:** x = 0
- **(d) Intercepts:**  
  - x-intercepts: (-2, 0), (2, 0)  
  - y-intercept: (0, 4)

Would you like more details or have any further questions? Here are some related problems for further practice:

1. How do you find the vertex of a parabola given its equation?
2. What is the general form of the equation of a parabola?
3. How does the direction of a parabola change when the leading coefficient changes?
4. Can a parabola have more than two x-intercepts? Why or why not?
5. How do you determine the y-intercept of a quadratic function from its equation?

**Tip:** The vertex form of a parabola \( y = a(x - h)^2 + k \) makes it easy to identify the vertex, which is \( (h, k) \).

Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? (b) Find the coordinates of the vertex. (c) Find the equation of the axis of symmetry. (d) Find the intercept(s).

Learn how to analyze the graph of a quadratic function to determine if it opens upward or downward, find the coordinates of the vertex, identify the equation of the axis of symmetry, and locate the x- and y-intercepts. Suitable for students in Grades 8-10.

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