To solve this, we need to analyze the graph of the quadratic function provided. We can observe that:

• The graph is a parabola that opens downward, meaning it has a maximum value at its vertex.
• The vertex is the highest point on the graph, which can be directly read off the grid.

Step-by-step solution:

1. Identify the vertex: The vertex is located at the point $(2, 8)$ from the graph.

2. Maximum value of $f(x)$: Since the maximum value of a parabola occurs at the vertex, the maximum value of $f(x)$ is the $y$-coordinate of the vertex, which is $8$.

Final Answer:

The maximum value of $f$ is 8.

Would you like further explanation on finding the vertex or any other aspect of this quadratic function?

Related Questions:

1. How do you calculate the x-intercepts of the quadratic function from the graph?
2. What is the axis of symmetry for this parabola, and how does it relate to the vertex?
3. How can you derive the quadratic equation from the graph if you know the x-intercepts and vertex?
4. What is the general form of the equation of a quadratic function, and how does it help in identifying the vertex?
5. How do you find the y-intercept from the graph of a quadratic function?

Tip:

For any quadratic function $f(x) = ax^2 + bx + c$, the x-coordinate of the vertex can be found using the formula $x = -\frac{b}{2a}$, which helps locate the maximum or minimum value.