Midterm Review Answers #23-43 Algebra 2H Midterm Review Answers #23-43

23) 𝑉𝑒𝑟𝑡𝑒𝑥:(0,−2). This has a maximum value because the leading coefficient is negative. 24) 𝐴) 𝑓(𝑥)=2(𝑥+6)(𝑥−2) B) 𝑔 𝑥 = −(𝑥+2 ) 2 +16 C)ℎ 𝑥 =2 𝑥 2 +11𝑥+12 Rewrite in Standard Form   𝑓 𝑥 =2 𝑥 2 +8𝑥−24 𝑔 𝑥 =− 𝑥 2 −4𝑥+12 Rewrite in Factored Form ℎ 𝑥 =(2𝑥+3)(𝑥+4) AOS: 𝑥=−2 AOS: 𝑥=−2 AOS: 𝑥=−2.75 𝑜𝑟− 11 4 Vertex: (−2,−32) Vertex: (−2,16) Vertex: −2.75,−3.125 𝑜𝑟(− 11 4 ,− 25 8 ) X-intercepts: −6,0 , (2,0) X-intercepts: −6,0 , (2,0) X-intercepts: − 3 2 ,0 , (−4,0) Y-intercept: (0,−24) Y-intercept: (0,12)

25) A) −3,∞ 𝑜𝑟 𝑥 𝑥≥−3} B) 4,∞ 𝑜𝑟 {𝑥|𝑥≥4} 26) Vertex: (−26, 50.7), so the maximum height of the soccer ball is 50.7 feet. 27) A) (2𝑥−1)(6𝑥+7) B) (𝑥+12)(𝑥−1)

28) If the discriminant is positive, then there are 2 real solutions 28) If the discriminant is positive, then there are 2 real solutions. If the discriminant is equal to zero, then there is 1 real solution. If the discriminant is negative, then there are no real solutions. 29) 𝑥=−5± 21 or 𝑥≈−.42 𝑎𝑛𝑑 𝑥≈−9.58 30) 𝑓 𝑥 →−∞𝑎𝑠 𝑥→∞ 𝑎𝑛𝑑 𝑓 𝑥 →∞𝑎𝑠 𝑥→−∞

A) 3 𝑥 2 −11𝑥−4 B) 2 𝑥 3 +5 𝑥 2 −23𝑥+10 A) 𝑥 3 −9 𝑥 2 +27𝑥−27 B) 𝑥 4 +4𝑥 3 +6 𝑥 2 +4𝑥+1 33) a) 𝑥=0, 𝑥=6, 𝑥=6 b) roots, x-intercepts, solutions c) zero, factor, factor, zero d) quadratic formula e) 𝑓 𝑥 =(𝑥+2)(𝑥+1)(𝑥−1)

34) a) ±1, ± 1 2 , ± 1 4 , ±2, ±5, ± 5 2 , ± 5 4 , ±10 b) 𝑥=−2, 𝑥=−1, 𝑥=2 35) 5 zeros   36) 𝑓 4 =−18 a) Graph 3 b) Graph 4 c) Graph 1 d) Graph 2

38) A) 𝑥+4 B) 3𝑥+2 39) a) Graph 1 b) Graph 4 c) Graph 3 d) Graph 2 40) x-intercepts: −.94,0 , 3.63,0 , (9.3,0) y-intercept: (0,95), local max: (1.04, 127.04) local min: 6.96, −185.04 The y-intercept represents the starting height of roller coaster. The local max represents the highest point the roller coaster achieves. The local min represents the lowest point the roller coaster achieves. The roller coaster is underground approximately 5.67 seconds (from 3.63 to 9.3 sec.).

40) Graph: