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 Materials axes, with or without technology. . grid paper or graphing f (x) = x2 f (x) = 2x2 f ( x) = -x2 technology 1 x2 f (x) = -2x2 f (x) = _ f (x) = -1x2 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) = ax2 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 Part B: Compare the Graphs of f(x) = x2 and f(x) = x2 + q 4. a) Graph the following functions on the same set of coordinate axes, with or without technology. f (x) = x2 f (x) = x2 + 4 f (x) = x2 - 3 b) Describe how the graph of each function compares to the graph of f (x) = x2. c) What relationship do you observe between the parameter, q, and the location of the corresponding graph? 5. a) Using a variety of values of q, write several of your own functions of the form A(x) = x2 + q. Include both positive and negative values. b) Predict how these functions will compare to f(x) = x2. Test your prediction. Reflect and Respond 6. Develop a rule that describes how the value of q in f(x) = x2 + q changes the graph of f(x) = x2 when q is b) a negative number a) a positive number Quadratic Functions in Vertex Form . MHR 143Part C: Compare the Graphs of f(x) = x2 and f(x) = (x - p)2 7. a) Graph the following functions on the same set of coordinate axes, with or without technology. f ( x) = x2 f (x) = (x - 2)2 f (x) = (x+1)2 b) Describe how the graph of each function compares to the graph of f(x) = x2. c) What relationship do you observe between the parameter, p, and the location of the corresponding graph? 8. a) Using a variety of values of p, write several of your own functions of the form f(x) = (x - p)2. Include both positive and negative values. b) Predict how these functions will compare to f(x) = x2. Test your prediction. Reflect and Respond 9. Develop a rule that describes how the value of p in f(x) = (x - p) changes the graph of f(x) = x2 when p is a) a positive number b) a negative number