AFOQT Practice Test

If a is positive in a quadratic equation, what direction does the graph open?

1. Downward

2. Upward

3. Sideways

4. Both upward and downward

The correct answer is: Upward

In a quadratic equation represented by the standard form \(y = ax^2 + bx + c\), the coefficient \(a\) plays a crucial role in determining the direction in which the graph opens. When \(a\) is positive, the parabola opens upward. This means that as you move away from the vertex in either direction along the x-axis, the value of \(y\) increases, creating a shape that resembles a "U". This behavior occurs because the positive coefficient indicates that as the squared term \(x^2\) dominates for larger values of \(x\) (both positive and negative), the output \(y\) will also become larger due to the squaring effect. In contrast, if \(a\) were negative, the graph would open downward, indicating that the values of \(y\) decrease as you move away from the vertex. The options about going sideways or both upward and downward do not apply to the nature of quadratic functions, which are defined specifically by their parabolic shape. Thus, the choice of "upward" is the only one that accurately describes the graph's behavior when \(a\) is positive.