https://file.aiquickdraw.com/mathbot/file/17325072861259n2ri840.jpg

Here is a solution based on the given graph of the parabola:

### (a) Does the parabola open upward or downward?
The parabola opens **downward**, as it has a maximum point (vertex) and the arms point downward.

### (b) Find the coordinates of the vertex.
From the graph, the vertex is located at the highest point of the parabola:
**Vertex: (2, 4)**.

### (c) Find the equation of the axis of symmetry.
The axis of symmetry is a vertical line passing through the vertex. Since the vertex's x-coordinate is \( x = 2 \), the equation is:
**Axis of symmetry: \( x = 2 \)**.

### (d) Find the intercept(s).
1. **x-intercepts**: These are the points where the parabola crosses the x-axis. From the graph, these are approximately:
**x-intercepts: (0, 0) and (4, 0)**.

2. **y-intercept**: This is the point where the parabola crosses the y-axis. From the graph, this is:
**y-intercept: (0, 0)**.

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If you need further clarifications or have any additional questions, feel free to ask!

Here are five follow-up questions for deeper understanding:
1. What is the general formula for the equation of a parabola in vertex form?
2. How do you verify the vertex coordinates algebraically?
3. What determines whether a parabola opens upward or downward in its equation?
4. How can you calculate the intercepts using the quadratic formula?
5. What role does the axis of symmetry play in analyzing a parabola?

**Tip:** Always double-check vertex and intercept values on graphs by substituting them into the equation of the parabola.

Use the graph of the parabola to answer the following: Does the parabola open upward or downward? Find the vertex, equation of the axis of symmetry, and the intercepts.

Learn how to analyze a parabola by identifying its vertex, equation of the axis of symmetry, and intercepts using a graph. Explore key quadratic concepts and properties of parabolas, suitable for Grades 8-10.

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