To explore the role of let’s use 0 for both and Then we will vary parameter until we can a, b c. a explain its role in the graph of . Case 1: 1 and = = 0 a b c ≥ Window settings: Xmin = Xmax = 4.7, Ymin = Ymax = 20. –4.7, –5, Let = 1, 2, and 3. Fill in the tables and draw all 3 functions on the same graph. a = = 2x2 = 3x2 y x2 y y x y x y x y –2 –2 –2 –1 –1 –1 0 0 0 1 1 1 2 2 2 The graphs you have drawn all have symmetry with respect to a vertical line. What vertical line? What is the equation of this line? What point do all three graphs have in common? Case 2: 0 < < 1 and 0 = = a b c Window settings: Xmin = Xmax = 4.7, Ymin = Ymax = 20. –4.7, –5, Let = .5, .25, and .1. Fill in the tables and draw all 3 functions on the same graph. a = .5x2 = .25x2 = .1x2 y y y x y x y x y –2 –2 –2 –1 –1 –1 0 0 0 1 1 1 2 2 2
To explore the role of a, let’s use 0 for both b and c. Then we will vary parameter a until we can explain its role in the graph of . Case 1: a ≥ 1 and b = c = 0 Window settings: Xmin = –4.7, Xmax = 4.7, Ymin = –5, Ymax = 20. Let a = 1, 2, and 3. Fill in the tables and draw all 3 functions on the same graph. y = x2 x y –2 –1 0 1 2 y = 2x2 x y –2 –1 0 1 2 y = 3x2 x y –2 –1 0 1 2 The graphs you have drawn all have symmetry with respect to a vertical line. What vertical line? What is the equation of this line? What point do all three graphs have in common? Case 2: 0 < a < 1 and 0 = b = c Window settings: Xmin = –4.7, Xmax = 4.7, Ymin = –5, Ymax = 20. Let a = .5, .25, and .1. Fill in the tables and draw all 3 functions on the same graph. y = .5x2 x y –2 –1 0 1 2 y = .25x2 x y –2 –1 0 1 2 y = .1x2 x y –2 –1 0 1 2
alg_u8_i1_a816_exploring_parameters_y.docx