https://file.aiquickdraw.com/mathbot/file/17294810336196p0koeqa.jpg

In the image, you are working on a problem related to quadratic functions. Specifically, you need to:

1. **Mark the vertex of the parabola.**
2. **Graph the axis of symmetry.**
3. **Write the coordinates of the vertex and the equation for the axis of symmetry.**
4. **Identify whether the graph has a maximum or minimum.**

Let's solve this step-by-step.

### Step 1: Analyze the graph

The parabola is facing **downward** (as indicated by its shape), which means it has a **maximum** value at the vertex. This suggests the quadratic function has a negative leading coefficient.

### Step 2: Vertex

From the graph, we can see the parabola's vertex is located at the point \((2, 4)\). This is the highest point on the graph.

- **Coordinate of the vertex:** \((2, 4)\)

### Step 3: Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex. Since the x-coordinate of the vertex is \(2\), the equation of the axis of symmetry is:

- **Equation of the axis of symmetry:** \(x = 2\)

### Step 4: Minimum or Maximum

Since the parabola opens downward, the vertex represents the **maximum** value of the function.

- **The function has a maximum.**

### Summary:

- **Vertex:** \((2, 4)\)
- **Axis of Symmetry:** \(x = 2\)
- **Maximum or Minimum:** Maximum

Let me know if you need more details or have any questions! 

Here are 5 follow-up questions for further practice:
1. How do you find the vertex of a quadratic equation from its standard form \(y = ax^2 + bx + c\)?
2. What is the formula for the axis of symmetry for any quadratic function?
3. How does the sign of the leading coefficient affect the direction of a parabola?
4. How can you determine if a quadratic function has a maximum or minimum based on its vertex form?
5. What role does the axis of symmetry play in graphing a quadratic function?

**Tip:** Always check if the parabola opens upwards or downwards to decide whether it has a maximum or minimum at the vertex!

For the parabola graphed below, mark the vertex with a dot and graph the axis of symmetry. Next, write the coordinates of the vertex and the equation for the axis of symmetry. Also identify if the graph has a maximum or minimum.

Solve the quadratic function problem by determining the vertex and the axis of symmetry. Identify if the parabola represents a maximum or minimum. Ideal for students in Grades 9-10 covering quadratic equations and graphing.

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