Vertex Form

Vertex form is a way to express a quadratic function that makes it easy to understand its graph's shape and position. It has the form \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex—the highest or lowest point on the parabola. The value \(a\) determines how wide or narrow the parabola is, and whether it opens upwards (positive \(a\)) or downwards (negative \(a\)). This form helps quickly identify the vertex location and the parabola's orientation, making graphing and analyzing quadratic functions more straightforward.