Investigate Graphs of Quadratic Functions in Vertex Form Part A: Compare the Graphs of f(x) = x2 and f(x) = ax2, a # 0 1. a) Graph the following functions on the same set of coordinate axes, with or without technology. f ( x) = x2 f (x) = -x2 f (x) = 2x2 f (x) = -2x2 f (x) = _x2 f (x) = -1, 5x2 b) Describe how the graph of each function compares to the graph of f(x) = x2, using terms such as narrower, wider, and reflection. c) What relationship do you observe between the parameter, a, and the shape of the corresponding graph? 2. a) Using a variety of values of a, write several of your own functions of the form f(x) = ax2. Include both positive and negative values. b) Predict how the graphs of these functions will compare to the graph of f(x) = x2. Test your prediction. Reflect and Respond 3. Develop a rule that describes how the value of a in f(x) = ax changes the graph of f(x) = x2 when a is a) a positive number greater than 1 b) a positive number less than 1 c) a negative number