Ohio Assessments for Educators (OAE) Mathematics Practice Exam

In the context of a parabola, which point represents the maximum or minimum of the function?

1. The vertex

2. The focus

3. The axis of symmetry

4. The directrix

The correct answer is: The vertex

In the context of a parabola, the vertex is the point that represents either the maximum or minimum of the function, depending on the direction in which the parabola opens. If the parabola opens upwards, the vertex represents the minimum point, as it is the lowest point on the graph. Conversely, if the parabola opens downwards, the vertex represents the maximum point, as it is the highest point on the graph. The vertex is significant as it provides crucial information about the shape and orientation of the parabola. The focus, while important for defining the parabola's shape, does not serve as a maximum or minimum point of the function. Similarly, the axis of symmetry is a vertical line that runs through the vertex and helps to determine the symmetry of the parabola but does not identify a maximum or minimum value on its own. The directrix is a fixed line used in conjunction with the focus to define the parabola, but it also does not represent a maximum or minimum of the function. Thus, the vertex is the key point in determining the extremum of a parabolic function, which directly relates to its algebraic representation as well as its graphical characteristics.