A parabola is a figure similar to the following:
In the example given the parabola opens downwards and the vertex acts as a maximum point. We can also have the following:
This parabola opens upwards and the vertex acts as a minimum point.
Now, the range is the values of the y-variable that the function outputs. We notice that in the first case, the range is the values that are smaller than the y-coordinate of the vertex.
In the second case, we notice that the range is the values that are greater than the y-coordinate of the vertex.
Therefore, we can conclude that the range is determined by the vertex, therefore, the right answer would be C.