Honors Mathematics 3 Practice Exam

The vertical shift comes from the constant added after the sine term. In y = a sin(bx - c) + d, that d moves the entire graph up or down by d, so it changes where the midline sits without changing the wave’s height or how stretched it is horizontally. In other words, the amplitude is governed by a, the period by b, and the horizontal position by c, while d sets the vertical position. If d is zero, there’s no vertical shift; positive d lifts the graph, negative d lowers it.