Rise and Run Property for Quadratic Functions Problem: The sum of consecutive odd

Chapter 7, Problem C.1

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Rise and Run Property for Quadratic Functions Problem: The sum of consecutive odd counting numbers is always a perfect square. For instance, 1 = 12 1 + 3 = 4 = 22 1 + 3 + 5 = 9 = 32 1 + 3 + 5 + 7 = 16 = 42 This fact can be used to sketch the graph of a quadratic function by a riserun technique similar to that used for linear functions. Figure 7-7c shows that for y = x2, you can start at the vertex and use the pattern over 1, up 1; over 1, up 3; over 1, up 5; . . . . a. On graph paper, plot the graph of y = x2 by using this riserun technique. Use integer values of x from 0 to 4. Then repeat the pattern for values of x from 0 to 4. b. y = 5 + (x 2)2 is a translation of the graph of y = x2. Locate the vertex, and then plot the graph on graph paper using the riserun pattern. c. y = 5 + 0.3(x 2)2 is a vertical dilation of the graph in part b. Use the riserun technique for this function, and then plot its graph on the same axes as in part b. Figure 7-7c