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!