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 $(h, k)$.