The coordinates (h, k) in vertex form represent what?

In the context of quadratic functions presented in vertex form, which is typically expressed as ( y = a(x-h)^2 + k ), the coordinates (h, k) specify the location of the vertex of the parabola. The vertex is a crucial point on the graph, representing the highest or lowest point of the parabola depending on the direction it opens (upward or downward).

Specifically, the value of 'h' indicates the x-coordinate of the vertex, while 'k' represents the y-coordinate. This tells us exactly where the vertex is situated in the Cartesian plane. The vertex is significant because it provides key information about the graph's shape and location. For instance, if the parabola opens upward (a positive "a"), the vertex (h, k) indicates the minimum point on the graph; conversely, if it opens downward (a negative "a"), this point represents the maximum.

Thus, identifying (h, k) in the vertex form directly leads to the conclusion that these coordinates describe the vertex of the quadratic function.