Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the vertex of a parabola given in the form a(x-h)² + k?

1. (h, k)

2. (k, h)

3. (h, 0)

4. (0, k)

The correct answer is: (h, k)

In the equation of a parabola written in the vertex form \( a(x-h)^2 + k \), the vertex is represented by the coordinates (h, k). This format allows you to identify the vertex directly: the value of \( h \) tells you the x-coordinate of the vertex, while the value of \( k \) gives you the y-coordinate. Therefore, the vertex of the parabola is indeed at point (h, k). Understanding this format is essential because it highlights how transformations affect the position of the parabola in the Cartesian plane. Other potential choices do not accurately represent the vertex's location: - The choice (k, h) swaps the coordinates, which is not the correct configuration. - The choice (h, 0) suggests that the y-coordinate of the vertex is zero, which is only true for specific cases and does not capture the general form of the vertex. - The choice (0, k) assigns the x-coordinate a value of zero, which again is not reflective of the vertex unless \( h \) happens to be zero, which is not guaranteed in this equation. Thus, affirming that the vertex format is critical for recognizing the parabola’s characteristics in its vertex form.