In the standard form of an absolute value function given by f(x) = a|x – h| + k, the vertex of the function is represented by the coordinates (h, k).
To break this down further:
- a: This coefficient affects the vertical stretch or compression of the absolute value graph. It also determines the direction of the graph’s opening. If a is positive, the graph opens upwards; if negative, it opens downwards.
- h: This value represents the x-coordinate of the vertex. It shows the horizontal shift from the origin. If h is positive, the graph shifts to the right; if negative, it shifts to the left.
- k: This number indicates the y-coordinate of the vertex. It leads to a vertical shift of the graph. A positive k shifts the graph upwards, while a negative k shifts it downwards.
In summary, the vertex of the absolute value function is crucial because it provides key information about the graph’s location in the coordinate plane. The vertex is the point where the graph changes direction, and its coordinates are (h, k). This makes it a vital point of reference when analyzing or graphing the function.