AFOQT Practice Test

What determines the direction in which the parabola opens?

1. The value of b

2. The value of a

3. The value of c

4. The vertex of the parabola

The correct answer is: The value of a

The direction in which a parabola opens is primarily determined by the value of "a" in its standard form equation, which is typically written as y = ax² + bx + c for a vertical parabola. When the value of "a" is positive, the parabola opens upwards, meaning it has a minimum point at its vertex and the arms extend infinitely upward. Conversely, when "a" is negative, the parabola opens downwards, indicating it has a maximum point at the vertex with the arms extending infinitely downward. The values of "b" and "c" affect the position and the shape of the parabola but do not influence the direction in which it opens. The vertex, while crucial for identifying the highest or lowest point of the parabola, is also not responsible for determining its opening direction. Therefore, the value of "a" is key to understanding the opening orientation of the parabola.