Final answer:
The vertex form of a quadratic function is useful because it reveals the parabola's vertex, aiding in graphing and solving quadratic equations, and showing the relationship to the basic quadratic function y = x².
Step-by-step explanation:
The vertex form of a quadratic function is a way of expressing the function that reveals the vertex of the parabola associated with it, which can provide insights into its relationship to the quadratic function y = x². The general vertex form is y = a(x-h)²+k, where (h, k) is the vertex of the parabola. Understanding this relationship helps in graphing the quadratic function and solving quadratic equations. The vertex form is useful because it allows us to easily identify the vertex of the parabola, which is a significant feature as it is the highest or lowest point on the graph, depending on whether the parabola opens upwards or downwards. Since y = x² is a special case of a quadratic function where the vertex is at the origin (0, 0), modifying the vertex form can shift the parabola vertically and horizontally to match any quadratic equation.