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? Based on Case 1 and Case 2, how does the graph change as gets larger? a Case 3: < 0 and = = 0 a b c Window settings: Xmin = Xmax = 4.7, Ymin = Ymax = 5. –4.7, –20, Let = and Fill in the tables and draw all 3 functions on the same graph. a –1, –2, –3. = = = y y y –x2 –2x2 –3x2 x y x y x y –2 –2 –2 –1 –1 –1 0 0 0 1 1 1 2 2 2 How do the graphs in case 3 differ from the graphs in 1 and 2? What do all the graphs in cases 1, 2, and 3 have in common? What the graph of look like In comparison with the graph of ? In comparison with the graph of ? Section 3: Exploring Parameter c Now that we have a good idea of how parameter impacts the graph of the function a we wish to explore the role of parameter So, we will keep and constant and then vary c. a b parameter until we can explain its impact. c Case 1: = 1 and = 0 and 0 a b c ≥
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? Based on Case 1 and Case 2, how does the graph change as a gets larger? Case 3: a < 0 and b = c = 0 Window settings: Xmin = –4.7, Xmax = 4.7, Ymin = –20, Ymax = 5. 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 How do the graphs in case 3 differ from the graphs in 1 and 2? What do all the graphs in cases 1, 2, and 3 have in common? What the graph of look like In comparison with the graph of ? In comparison with the graph of ? Section 3: Exploring Parameter c Now that we have a good idea of how parameter a impacts the graph of the function we wish to explore the role of parameter c. So, we will keep a and b constant and then vary parameter c until we can explain its impact. Case 1: a = 1 and b = 0 and c ≥ 0
alg_u8_i1_a816_exploring_parameters_y.docx