From the uploaded image of the parabola and table, I will analyze the graph and provide the required information.

(a) Does the parabola open upward or downward?

The parabola opens downward, as the arms of the parabola point down.

(b) Find the coordinates of the vertex.

The vertex is the highest point of the parabola. From the graph, the vertex is at (0, 4).

(c) Find the equation of the axis of symmetry.

The axis of symmetry is the vertical line passing through the vertex. Since the vertex is at $x = 0$, the equation of the axis of symmetry is: $x = 0$

(d) Find the x-intercept(s).

The x-intercepts are the points where the parabola crosses the x-axis. From the graph, the parabola crosses the x-axis at $x = -2$ and $x = 2$. Therefore, the x-intercepts are: $x = -2, 2$

Completed Table:

• (a) Downward
• (b) Vertex: $(0, 4)$
• (c) Axis of symmetry: $x = 0$
• (d) X-intercepts: $-2, 2$

Would you like further explanation or additional calculations?
Here are 5 questions related to this content to expand understanding:

1. What is the significance of the vertex in a parabola's equation?
2. How do you find the vertex from a quadratic equation?
3. How can you determine if a parabola opens upward or downward from its equation?
4. Why is the axis of symmetry always a vertical line for parabolas?
5. How do you calculate the x-intercepts algebraically?

Tip: The vertex form of a parabola, $y = a(x-h)^2 + k$, is a helpful way to identify the vertex $(h, k)$ and the direction of the parabola!