Now summarize the role of parameter when > 0 or < 0. c c c Section 4: Exploring Parameter b Now let’s keep parameters and constant and then vary parameter until we can explain its a c b impact. Case 1: = 1 and = 0 and 0 a c b ≥ Window settings: Xmin = Xmax = 4.7, Ymin = Ymax = 4. –4.7, –4, Let = 0, 2, and 4. Fill in the tables and draw all 3 functions on the same graph. b = = + 2x = + 4x y x2 y x2 y x2 x y x y x y –2 –2 –2 –1 –1 –1 0 0 0 1 1 1 2 2 2 What can you say about the location of the vertex when > 0? b What happens to the location of the vertex as gets larger? b When > 0, the graph should still have symmetry but the line of symmetry is now a different b vertical line. Try to find the equation of each line of symmetry and write the equations here. Case 2: = 1 and = 0 and < 0 a c b Window settings: Xmin = Xmax = 4.7, Ymin = Ymax = 4. –4.7, –4, Let = and Fill in the tables and draw all 3 functions on the same graph. b –2, –3, –4. 3 = 2x y x2 – = 3x y x2 x y – x y = 4x y x2 –2 – –2 x y –1 0 –1 –2 0 1 –1 1 2 0 2 3 1
Now summarize the role of parameter c when c > 0 or c < 0. Section 4: Exploring Parameter b Now let’s keep parameters a and c constant and then vary parameter b until we can explain its impact. Case 1: a = 1 and c = 0 and b ≥ 0 Window settings: Xmin = –4.7, Xmax = 4.7, Ymin = –4, Ymax = 4. Let b = 0, 2, and 4. Fill in the tables and draw all 3 functions on the same graph. y = x2 x y –2 –1 0 1 2 y = x2 + 2x x y –2 –1 0 1 2 y = x2 + 4x x y –2 –1 0 1 2 What can you say about the location of the vertex when b > 0? What happens to the location of the vertex as b gets larger? When b > 0, the graph should still have symmetry but the line of symmetry is now a different vertical line. Try to find the equation of each line of symmetry and write the equations here. Case 2: a = 1 and c = 0 and b < 0 Window settings: Xmin = –4.7, Xmax = 4.7, Ymin = –4, Ymax = 4. Let b = –2, –3, and –4. Fill in the tables and draw all 3 functions on the same graph. y = x2 – 2x x y –2 –1 0 1 2 3 y = x2 – 3x x y –2 –1 0 1 2 3 y = x2 – 4x x y –2 –1 0 1