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### (a) **Does the parabola open upward or downward?**
- Since the parabola's vertex is at the top and the arms extend downward, **it opens downward**.

### (b) **Find the equation of the axis of symmetry**
- The axis of symmetry is the vertical line that passes through the vertex. This line's equation is of the form \( x = h \), where \( h \) is the x-coordinate of the vertex.
- From the graph, the x-coordinate of the vertex seems to be around \( x = 2 \), so the axis of symmetry is:
  \[
  \text{Axis of symmetry: } x = 2
  \]

### (c) **Find the coordinates of the vertex**
- The vertex is the highest point of the parabola. From the graph, it looks like the vertex is at the point \( (2, 4) \).
  \[
  \text{Vertex: } (2, 4)
  \]

### (d) **Find the intercept(s)**
1. **x-intercepts:** These are the points where the parabola crosses the x-axis. It seems the parabola crosses the x-axis at \( x = 0 \) and \( x = 4 \).
   \[
   \text{x-intercepts: } 0, 4
   \]
2. **y-intercept:** The parabola crosses the y-axis at \( y = 0 \), so:
   \[
   \text{y-intercept: } (0, 0)
   \]

Would you like more details or clarification on any part of this solution?

### Additional Questions:
1. How do you determine whether a parabola opens upward or downward based on its graph?
2. What is the significance of the axis of symmetry for a parabola?
3. How can you find the vertex of a parabola using its equation in standard form?
4. How would you calculate x-intercepts algebraically if the equation of the parabola is given?
5. How is the vertex related to the maximum or minimum value of a quadratic function?

#### Tip:
When finding the axis of symmetry, it always corresponds to the x-value of the vertex of the parabola, regardless of whether it opens upward or downward.

Find the vertex, intercepts, and axis of symmetry from the graph of a parabola.

Learn how to find the vertex, intercepts, and axis of symmetry from a graph of a parabola. This detailed explanation covers essential algebraic concepts, including identifying the vertex at (2, 4), calculating the axis of symmetry as x = 2, and finding the x-intercepts and y-intercepts.

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