Ohio Assessments for Educators (OAE) Mathematics Practice Exam

In the vertex form of a parabola, what does 'h' and 'k' represent?

1. The coordinates of the vertex

2. The coefficients of the quadratic

3. The axis of symmetry values

4. The roots of the equation

The correct answer is: The coordinates of the vertex

In the vertex form of a parabola, which is expressed as \( y = a(x - h)^2 + k \), the values "h" and "k" uniquely identify the coordinates of the vertex of the parabola. The vertex is the point at which the parabola changes direction and is either the highest or lowest point, depending on the direction in which the parabola opens (upward or downward). Specifically, "h" represents the x-coordinate of the vertex, while "k" indicates the y-coordinate. For example, if \( h = 3 \) and \( k = 2 \), the vertex of the parabola is located at the point (3, 2). Recognizing the vertex helps in graphing the parabola and understanding its properties, such as its maximum or minimum values and the line of symmetry. The other options, while related to the characteristics of a quadratic function, do not accurately describe the specific roles of "h" and "k" in the vertex form. The coefficients of the quadratic affect the width and direction of the parabola, the axis of symmetry is determined by the x-coordinate of the vertex, and the roots are the solutions to the equation where the parabola