What is the vertex form of a quadratic function?

The vertex form of a quadratic function is indeed represented by the equation that includes a perfect square term, specifically structured as (y = a(x - h)^2 + k). In this equation, (a) determines the direction and width of the parabola (opening upwards if (a) is positive, downwards if negative), while the values (h) and (k) represent the coordinates of the vertex of the parabola. This form is particularly useful because it allows for easy identification of the vertex, enabling us to quickly understand the key characteristics of the graph, including its maximum or minimum point.

By contrast, the other forms listed do not provide the same immediate insight into the vertex. The standard form of a quadratic function, which might be represented as (y = ax^2 + bx + c), does not clearly showcase the vertex without further manipulation. The equation (y = a(x + h)^2 + k) changes the sign of (h), which can lead to confusion when identifying the vertex. Finally, (y = ax^2 + c) represents a specific case of a quadratic where the coefficient (b) is zero, which limits its applications and neglects the general