What does 'k' correspond to in vertex form?

In the vertex form of a quadratic function, which is expressed as ( f(x) = a(x - h)^2 + k ), the variable 'k' represents the y-coordinate of the vertex of the parabola. This point is critical because it provides important information about the graph of the quadratic function, particularly its maximum or minimum value.

The vertex ( (h, k) ) serves as the highest or lowest point on the graph depending on the value of 'a' (the coefficient in front of the squared term). If 'a' is positive, the parabola opens upwards and 'k' will be the minimum value of the function. Conversely, if 'a' is negative, the parabola opens downwards and 'k' will be the maximum value.

This means that 'k' directly corresponds to the output of the function at the vertex, which is indeed denoted by ( f(h) ). Therefore, in the context of vertex form, 'k' reflects the vertical positioning of the parabola at its vertex, encapsulating essential characteristics of the quadratic function.