advanced algebra d
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Advanced Algebra D. Chapter 6 Review. Find the zeros and their multiplicity: f(x) = - 3x 6 - x 5 + 10x 4. 0 m4, 5/3 m1, 2 m1 0 m1, 5/3 m1, -2 m1 0 m4, 3 m1, -2 m1 0 m1, -3 m1, 2 m1 0 m4, -5/3 m1, 2 m1 0 m4, 5/3 m1, -2 m1 None of the above. - PowerPoint PPT PresentationTRANSCRIPT
Advanced Algebra D
Chapter 6 Review
Find the zeros and their multiplicity:f(x) = - 3x6 - x5 + 10x4
1 2 3 4 5 6 7
0% 0% 0% 0%0%0%0%
1. 0 m4, 5/3 m1, 2 m12. 0 m1, 5/3 m1, -2 m13. 0 m4, 3 m1, -2 m14. 0 m1, -3 m1, 2 m15. 0 m4, -5/3 m1, 2 m16. 0 m4, 5/3 m1, -2 m17. None of the above
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Find the end behavior: f(x) = - 3x6 - x5 + 10x4
1 2 3 4
0% 0%0%0%
1. 2. 3. 4.
lim ( )1.
lim ( )
lim ( )2.
lim ( )
lim ( )3.
lim ( )
lim ( )4.
lim ( )
x
x
x
x
x
x
x
x
f x
f x
f x
f x
f x
f x
f x
f x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Determine the relative minimum(s) and relative maximum(s) f(x) = - 3x6 - x5 + 10x4
1 2 3 4
0% 0%0%0%
1. Max: (-1.64, 25.84)Min: (0, 0)
2. Max: (1.36, 10.57)Min: (0,0)
3. Max: (-1.64, 25.84)Max: (1.36, 10.57)
4. None of the above
Correct Answer:Max: (-1.64, 25.84)Max: (1.36, 10.57)Min: (0, 0)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
A zero with even multiplicity
1 2 3 4 5
0% 0% 0%0%0%
1. Touches the x-axis and bounces away
2. Crosses the x-axis3. Never hits the x-axis4. Both 1 & 25. None of the above
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
A zero with odd multiplicity
1 2 3 4 5
0% 0% 0%0%0%
1. Touches the x-axis and bounces away
2. Crosses the x-axis3. Never hits the x-axis4. Both 1 & 25. None of the above
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Write a polynomial function in factored form with zeros 3 m1, -2 m2, 4/5 m1
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
2
2
1. ( ) 3 2 5 4
2. ( ) 3 2 5 4
3. ( ) 3 2 5 4
4. ( ) 3 2 5 4
5. None of the above
f x x x x
f x x x x
f x x x x
f x x x x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Write a polynomial function in STANDARD form with zeros 3 m1, -2 m2, 4/5 m1
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
2
4 3 2
4 3 2
3 2
4 3 2
1. ( ) 3 2 5 4
2. ( ) 5 44 28 48
3. ( ) 5 19 32 76 48
4. ( ) 5 9 26 24
5. ( ) 5 39 98 124 48
6. None of the above
f x x x x
f x x x x x
f x x x x x
f x x x x
f x x x x x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Solve for ALL solutions.0 = 27x3 + 125
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
51.
3
5 5 5 32. ,
3 6
5 5 5 33. ,
3 65 80
4. ,3 27
5. None of the above
x
ix
ix
x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Solve for ALL solutions.0 = x4 – 14x2 + 45
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
1. 3, 5
2. 9, 5
3. 3 , 5
4. 3, 5
5. None of the above
x
x
x i i
x i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Solve for ALL solutions.0 = x3 + 2x2 - 2x - 4
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
1. 2
2. 2, 2
3. 2, 2
4. 2, 2
5. None of the above
x
x i
x
x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Find the quotient and remainder(x5 + x4 - 13x3 - 13x2 + 36x + 36) / (x2 - 4)
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
4 3 2
3 2
3 2
3 2
1. 5 7 15 96; 420
2. 17 17; 104 104
3. 5 7 15; 24 36
4. 9 9; 0
5. None of the above
x x x x R
x x x R x
x x x R x
x x x R
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
List all possible rational roots:f(x) = 6x3 + 5x2 - 3x + 15
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
1. 1,3,5,15
1 3 5 15 1 5 1 52. 1,3,5,15, , , , , , , ,
2 2 2 2 3 3 6 6
3. 1,2,3,6
1 2 1 2 3 6 1 24. 1,2,3,6, , , , , , , ,
3 3 5 5 5 5 15 15
5. None of the above
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Find ALL zeros.f(x) = 2x4 - x3 + 7x2 - 5x - 15
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
31. 1, , 5
2
7 1432. 1, 2,
4
1 953. 1,2,
43
4. 1, , 102
5. None of the above
x i
ix
ix
x i
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Write a polynomial function in factored form with zeros
1 2 3 4 5
0% 0% 0%0%0%
1. 2. 3. 4. 5.
1. ( ) 3 3 3 3 5 5
2. ( ) 3 3 3 3 5 5
3. ( ) 3 3 5
4. ( ) 3 3 5
5. None of the above
f x x i x i x x
f x x i x i x x
f x x i x
f x x i x
3 3 , 5i
Correct Answer:
( ) 3 3 3 3 5 5f x x i x i x x
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
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Box Problem
• Advanced Algebra Students, Inc. is designing cardboard boxes without a top. The boxes will be made from a single sheet of cardboard where the corners will be cut out, then folded up to make a box.
Box Problem
• The company wants to maximize the volume of the box. To do so, you decide to write a function that would describe the total volume of the box given the length “x” of one side of the cutout.
Box Problem
• The company wants to maximize the volume of the box. To do so, you decide to write a function that would describe the total volume of the box given the length “x” of one side of the cutout.
Box Problem
• You are given the original sheet of cardboard is 12 inches X 20 inches
Box Problem
• You are given the original sheet of cardboard is 12 inches X 20 inches
Box Problem
• With your partner write a function to describe the volume “V(x)” based on the length of the cutout “x”
Box Problem
• V = L*W*H• H = x• L = 20 – 2x• W = 12 – 2x• V(x) = (20-2x)(12-2x)x
Box Problem
• Use your calculator to determine the maximum volume of the function
• Coordinates of Relative Maximum:(2.43, 262.68)
• Thus the maximum volume is 262.68 in3
Box Problem
• What would be the dimensions of the box that would produce that maximum volume?
• H = 2.43• L = 20-2(2.43) = 15.15• W = 12-2(2.43) = 7.15• 15.15in x 7.15in x 2.43in