b. =2; = a b –82 x b 87. = 5x2 + 40x + 600 y = − 20.5 −82 = x = −b = −40 = −4 =− 2a 10 2a 4 2(20.5)2 82(20.5) y = − + = 5(–4)2 + 40(–4) + 600 y 720 = 80 160 + 600 = 520 840.5 720 – = −1681 + vertex: (–4, 520) = −120.5 vertex: (20.5, –120.5) c. Ymax = 750 d. You can choose Xmin and Xmax so the x-value of the vertex is in the center of the graph. Choose Ymin to include the of the y-value vertex. 85. = + 40x y –0.25x2 x = −b = −40 = = 0.01x2 + 0.6x + 100 88. y 80 2a −0.5 −b −0.6 = + 40(80) y –0.25(80)2 = 1600 x = = = −30 2a 0.02 2 vertex: (80, 1600) = 0.01(–30) + 0.6(–30) + 100 y 18 + 100 = 91 The vertex is at (–30, 91). 86. = + 20x + 160 y –4x2 89. a. The values of increase then decrease. y 2.5 x = −b = −20 = = 9 – 2a −8 = + 20(2.5) + 160 y –4(2.5)2 = + 50 +160 = 185 –2.5 The vertex is at (2.5, 185). b. 6.17x 9.57 y = −0.48x2 + + c. 6 x = −(6.17) ≈ 2(−0.48) 6.17(6) 9.57 y = −0.48(6)2 + + ≈ 29.3 According to the model in part (b), American had the greatest number of viewers, 29.3 Idol million, in Season 6.
b. a =2; b = –82 x = − b −82 = 20.5 87. y = 5x2 + 40x + 600 x = −b = −40 = −4 =− 2a 4 2a 10 y = 2(20.5)2 − 82(20.5) + 720 y = 5(–4)2 + 40(–4) + 600 = 840.5 −1681 + 720 = −120.5 = 80 – 160 + 600 = 520 vertex: (–4, 520) vertex: (20.5, –120.5) c. Ymax = 750 d. You can choose Xmin and Xmax so the x-value of the vertex is in the center of the graph. Choose Ymin to include the y-value of the vertex. 85. y = –0.25x2 + 40x x = −b = −40 = 80 88. y = 0.01x2 + 0.6x + 100 2a −0.5 −b −0.6 y = –0.25(80)2 + 40(80) = 1600 x = = = −30 2a 0.02 2 vertex: (80, 1600) y = 0.01(–30) + 0.6(–30) + 100 86. y = –4x2 + 20x + 160 x = −b = −20 = 2.5 = 9 – 18 + 100 = 91 The vertex is at (–30, 91). 89. a. The values of y increase then decrease. 2a −8 y = –4(2.5)2 + 20(2.5) + 160 = –2.5 + 50 +160 = 185 The vertex is at (2.5, 185). b. y = −0.48x2 + 6.17x + 9.57 c. x = −(6.17) ≈ 6 2(−0.48) y = −0.48(6)2 + 6.17(6) + 9.57 ≈ 29.3 According to the model in part (b), American Idol had the greatest number of viewers, 29.3 million, in Season 6.
Precalculus-Essentials-5th-Edition-Blitzer-Solutions-Manual.docx