Chapter 5: Exercises with Solutions

Section 5.1The Parabola5.1 Solutions1. First, enter the functions into the Y= menu. Then press GRAPH to view a comparisonof the three graphs.Note how the graph of y = 2x 2 is narrower and taller than the graph of y = x 2 , andthe graph of y = 4x 2 is narrower and taller still. We see therefore that multiplying x 2by a positive number such as 2 or 4 stretches or scales the graph vertically, making ittaller (and narrower).3. First, enter the functions into the Y= menu. Then press GRAPH to view a comparisonof the three graphs.Note how the graph of g(x) = (x−2) 2 has the same shape as the graph of f(x) = x 2but it is shifted 2 units to the right; and the graph of h(x) = (x − 4) 2 also has the sameshape, but is shifted 4 units to the right. It thus appears that y = (x − c) 2 , for positivec, has the same shape as f(x) = x 2 but is shifted c units to the right.Version: Fall 2007