Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the direction of the parabola when the coefficient 'a' in the quadratic equation ax² + bx + c is positive?

1. Opens upward

2. Opens downward

3. No specific direction

4. Flattens

The correct answer is: Opens upward

When the coefficient 'a' in the quadratic equation ax² + bx + c is positive, the parabola opens upward. This is a fundamental characteristic of quadratic functions. In the graph of a quadratic function, the term 'x²' dictates the curvature of the parabola. If 'a' is positive, the values of the quadratic expression increase as 'x' moves away from the vertex in both directions (left and right). As a result, the lowest point of the parabola, known as the vertex, will serve as a minimum point, and the arms of the parabola will extend upwards. This upward opening implies that for very large or very small values of 'x', the function yields larger positive values, reinforcing the visual representation of the parabola resembling a "U" shape, which is indicative of upward direction. In contrast, when 'a' is negative, the parabola opens downward, creating a "n" shape, and the vertex would be a maximum point. Other options that mention "no specific direction" or "flattens" do not accurately represent the behavior of parabolas based on the sign of 'a'. Thus, understanding the role of the coefficient 'a' is crucial in determining