The image shows a graph of a quadratic function $f(x)$ along with a set of labeled points. The question asks to identify the coordinates of the vertex of the parabola from the given options.

The vertex of a parabola is the point where the function reaches its maximum or minimum value, depending on whether it opens upwards or downwards. In this case, the parabola opens upwards (since the graph shows a "U" shape), so the vertex represents the minimum point.

From the graph, the vertex appears to be at the point where $x = 0$ and $y = 1$, which is $(0, 1)$.

Answer: The vertex is at $(0, 1)$, which corresponds to Option (d).

Let me know if you want more details or have questions.

Related Questions:

1. What is the general formula for the vertex of a parabola given its equation?
2. How do you find the vertex of a parabola algebraically?
3. What does the sign of the coefficient of $x^2$ tell you about the direction a parabola opens?
4. How can you calculate the axis of symmetry from a quadratic function?
5. How does changing the vertex affect the graph of a parabola?

Tip:

The vertex form of a quadratic function is $f(x) = a(x-h)^2 + k$, where $(h, k)$ is the vertex.