Graph the following points on the graphing calculator:Explain how to use the graph to write an equation to model the gum’s height. Be sure to identify the pattern of the points in your explanation, and identify the values of a and k.

Answer:

The pattern is min-zero-max-zero-min, which is the pattern for a cosine function of the form y = acos(x) + k, but is reflected over the x-axis (so a < 0). The amplitude is |a|, so a = –1 and |a| = 1. The midline is exactly between the max and the min, y = (6 + 8)/2 = 7, so k = 7. The equation is y = –cos(x) + 7.