Selected AnswersTopic 2PearsonRealize.com18. y=x2-3x+720. Answers may vary. Sample: Calculate the vertex to find the maximum height of the ball. You can use the vertex to find the horizontal distance from the starting point and multiply by 2 to find the total distance. 22. x=-3 or x=924. x=-1.5 or x=0.526. x<-5 or x>628. x-630.13 -i32.3__2-1__2i34.They did not change i2VQ Ũ±¹µ¸ Ũ ²i)(4 +i ) =±± Ũ ±ºi36.(x-8) 2=28 38.x=12 ±ū____22640. x=2 ±ū___41 ____242.5.04 seconds; The other root is negative, which is not an appropriate value for this situation. 44. x=8 ± 2 ū___1046.x=9 ± ū___71 _______248.2 real solutions 50.k=± 8 52.below 25 kilometers per hour and above 79 kilometers per hour 54.0y8642Ox121256.(-1, 6), (0, 7)enVision™Algebra 2|12| Selected Answers
Selected AnswersTopic 3PearsonRealize.comLesson 3-12.Allie did not write the polynomial function in standard form; instead, she said the exponent of the first term was the degree of the polynomial. The degree is 6. 4.For a polynomial function with an even degree, as x-and x+, y-values either both approach +or both approach -. If the leading coefficient is positive, both ends approach +. If negative, both ends approach -. A polynomial function with an odd degree has end behavior for positive and negative xin opposite directions. If the leading coefficient is positive, as x-, y–, and as x+, y+. If the leading coefficient is negative, the end behavior is in the opposite direction. 6.4 8.As x-, y+. As x+, y+. 10.x=-4, x=-2, x=1, x=3 12.approximately (-0.5, 28) 14.f(x) =-2x 5+2x 4-2x 3+x 2-x+1; The polynomial function must have a negative leading coefficient and an odd degree because of the end behavior. The function must have a degree of at least 5 because there are 6 terms. The last term of the function is 1 because the y-intercept is (0, 1).yOx424242416.Check students’ graphs. Sample:yOx42424242yOx4242121yOx4242424218.f(x) =2x 5+x 4+5x 3-3x 2+x-6; 5; 6; 2 20.f(x) =–x 4-x 3+5x 2+9x+12; 4; 5; –1 22.The leading coefficient, 7, is positive, so the graph opens upward. The degree is 4, which is even, so the end behaviors are the same. As xbecomes infinitely positive or negative, the y-values approach +.enVision™Algebra 2|13| Selected Answers
Selected AnswersTopic 3PearsonRealize.com24.zeros: x= -3, x= -1, x=2; turning points between -3 and -1, between -1 and 2yOx44288426.yOx4420101028. a.f(x) =4x 3-38x 2+88xb.reasonable domain: 0 <x<4yOx462220204060c. x-intercepts: 0, 4, and 5.5; 0 and 4 represent the side lengths of the cut squares that will result in a box with 0 volume. The intercept at 5.5 is not meaningful, because it is not possible to cut two 5.5-inch corners from an 8-inch side. d.About 1.5 in. will create a box with a volume of about 60 in.