What is the vertex form of a quadratic function?

The vertex form of a quadratic function is expressed as (y = a(x - h)^2 + k). In this form, (a) represents the coefficient that affects the width and direction of the parabola, while the point ((h, k)) denotes the vertex of the parabola. This means that ((h, k)) gives both the highest or lowest point on the graph, depending on the sign of (a). When the quadratic is in vertex form, it becomes easier to analyze features such as the vertex's location and the direction in which the parabola opens (upward or downward based on the sign of (a)).

This form is particularly useful for graphing the quadratic function, as one can quickly identify where the parabola will peak or trough, making it a vital concept in quadratic relationships.