Final answer:
Without a graph or an equation of the function, it is not possible to determine the vertex among the provided options. The vertex of a quadratic function is either a maximum or minimum point on the graph, found at the point where the parabola changes direction. Further information like the graph or an equation in vertex form is needed to identify the vertex accurately.
Step-by-step explanation:
The question asks to identify the vertex of the function graphed with the given options. To determine which one could be the vertex, we need to look at a graph. However, the provided data points (1,5), (2,10), (3,7), and (4,14) suggest that this is not a graph of a quadratic function since the points do not form a parabola. When graphing these points, one can see that they do not create a curve with a maximum or minimum point, which is typical of quadratic functions where the vertex is found. Instead, these data points may suggest a different type of function.
The vertex of a function, typically a quadratic function, is the highest or lowest point of the graph known as the maximum or minimum. In a parabola that opens upwards, the vertex is the minimum point; in one that opens downwards, it is the maximum. If we had the graph of a parabola, we would look for the point where the parabola changes direction. Without the graph or an equation, we cannot confirm the vertex among the given options; they are simply points that may or may not lie on the graph of the actual function. To identify a vertex, one usually needs either the graph of the function or its equation in vertex form, which appears as f(x) = a(x-h)^2 + k where (h, k) is the vertex.