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Table of Contents Introduction In this investigation quartic functions will be explored, in particular quartic functions with a unique "W" shape. These quartic functions will have two points of inflection, which will be referred to as Point Q and Point R. When Line QR is drawn it intercepts the quartic function twice more; those interceptions will be referred to as Point P and Point S. The ratio of PQ:QR:RS will be investigated and any findings will be formally proven. This investigation will include the given function f(x) = x4 - 8x3 + 18x2 - 12x +24 and the chosen function f(x) = x4 + 3x3 -5x . These functions will be depicted with graphs. Method 1. Graph the function f(x) = x4 - 8x3 + 18x2 - 12x +24. 2. Find the coordinates of the points of inflection Q and R. Determine the points P and S, where the line QR intersect the quartic function...

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