Unit #8 Radicals and The Quadratic Formula
Name: ____________________________________
Date: ________________________
UNIT #8 – RADICALS AND THE QUADRATIC FORMULA COMMON CORE ALGEBRA II Part I Questions 1. Given that both a and b are positive numbers, which of the following equations would describe the graph shown below given that it is a transformation of the graph of y x . (1) y x a b (2) y x a b (3) y x a b (4) y x a b 2. Which of the following represents the domain of the function f x 3 x 2 ? (1) x 2
(3) x
2 3
(2) x 2
(4) x
2 3
3. If the function y x 3 5 is defined only on the domain 3 x 19 , then which of the following represent its range?
(1) y 5
(3) 3 y 4
(2) 5 y 9
(4) 5 y 16
4. Which of the following is the solution set to: x 2 x 15 ? (1) x 5
(3) x 3
(2) x 3 and 5
(4) x 5 and 3
5. If f x 2 x 5 11 then for which value of x is f x 14 ? (1) 7 14
(3) 3 12
(2) 5 34
(4) 2 12 COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
x The expression
3 2
6.
x x 2
5
can be written at
1 , where k is some integer. Which of the following represents the xk
value of k? (1) 16
(3) 6
(2) 13
(4) 4
7. The expression
2x can be written equivalently as 16 x
(1) 2 x 4
1 (3) 8
(2) 2 x 16
(4) 32 x
8. The radical expression 3 135x 4 y 8 can be simplified to
(1) 45xy 2 3 x
(3) 3 xy 2 3 27 xy
(2) 5 x 2 y 3 3 y 2
(4) 3xy 2 3 5 xy 2
9. The expression x 1/ 4 is the same as (1)
(2)
x 4
(3)
1 x4
(4)
x 10. The expression 4
(1) (2)
4
x3
1 x
3
x7
1 x
4
1 x4
5
can be written, for x 0 , as
x5
(3) (4)
1 4
x9
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
11. Which of the following is the simplified version of (1)
(2)
1 x
5
1 3 x
6
?
(3) x 2
1 x
(4) x 7
12. Which of the following represents the solution set to: 2 x 5 7 29 ? 2
29 2
(1) 5
(2) x 3 and 7
(3) x 2 and 8 (4) x 5 18
13. Which of the following represent the roots of the equation 2 x 2 6 x 1 0 ? (1) x 6 11
3 (3) x 2 11 2
3 11 (2) x 2 2
(4) 3 11
14. What are the zeroes of f x 6 x 2 31x 40 ? 31 543 12
(1) x
5 8 and 2 3
(3) x
(2) x
31 5 29 12
(4) x
3 5 and x 2 3
15. The larger root of the equation 3 x 2 5 x 1 0 is closest to (1) 1.43
(3) 2.57
(2) 1.87
(4) 3.19 COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
Free Response Questions
16. Given the function f x x 2 3 answer the following: (a) Graph the function on the grid shown.
(b) Explain how the graph of y x has been transformed into the graph of f x .
(c) What are the domain and range of f x ? Domain:
Range:
17. Solve the equation shown below algebraically. Be sure to check your solutions!!! x 2 19 2 x
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
18. Consider the function g x 2 x 2 5 x 12 . (a) Is x 1 a member of the natural domain of this function? Justify your yes/no response.
(b) Write an inequality that models the natural domain of this function. Explain how you arrived at your inequality.
(c) Algebraically solve the inequality you wrote in (b) to determine the natural domain of this function. Verify graphically and sketch a graph of g x on the axes below.
19. Jaylen and his brother Tyler are both in Algebra II and are debating a question about roots. Jaylen believes that taking the square root of a number and then the cube root of the result is the same as just taking the sixth root of the number. Tyler disagrees and believes that the combination of these two roots results in a fifth root. Who is correct and why?
20. Write
4
80x9 y16 in simplest radical form. Show how you arrived at your answer.
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
21. A projectile is fired vertically from an initial height of 8 feet with an initial velocity of 340 feet per second. Its height above the ground in feet can be modeled as a function of time by the equation h t 16t 2 340t 8
where t represents the seconds since fired
(a) Determine, algebraically, when the projectile hits the ground to the nearest tenth of a second.
(b) Write an inequality and solve it algebraically to determine all times at which the projectile is at or above 1,000 feet. Round all times to the nearest tenth of a second.
22. Solve the following system of equations algebraically. y x 10 1 y 2x 9
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
Date: ________________________
UNIT #8 – RADICALS AND THE QUADRATIC FORMULA COMMON CORE ALGEBRA II Part I Questions 1. Given that both a and b are positive numbers, which of the following equations would describe the graph shown below given that it is a transformation of the graph of y x . (1) y x a b (2) y x a b (3) y x a b (4) y x a b 2. Which of the following represents the domain of the function f x 3 x 2 ? (1) x 2
(3) x
2 3
(2) x 2
(4) x
2 3
3. If the function y x 3 5 is defined only on the domain 3 x 19 , then which of the following represent its range?
(1) y 5
(3) 3 y 4
(2) 5 y 9
(4) 5 y 16
4. Which of the following is the solution set to: x 2 x 15 ? (1) x 5
(3) x 3
(2) x 3 and 5
(4) x 5 and 3
5. If f x 2 x 5 11 then for which value of x is f x 14 ? (1) 7 14
(3) 3 12
(2) 5 34
(4) 2 12 COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
x The expression
3 2
6.
x x 2
5
can be written at
1 , where k is some integer. Which of the following represents the xk
value of k? (1) 16
(3) 6
(2) 13
(4) 4
7. The expression
2x can be written equivalently as 16 x
(1) 2 x 4
1 (3) 8
(2) 2 x 16
(4) 32 x
8. The radical expression 3 135x 4 y 8 can be simplified to
(1) 45xy 2 3 x
(3) 3 xy 2 3 27 xy
(2) 5 x 2 y 3 3 y 2
(4) 3xy 2 3 5 xy 2
9. The expression x 1/ 4 is the same as (1)
(2)
x 4
(3)
1 x4
(4)
x 10. The expression 4
(1) (2)
4
x3
1 x
3
x7
1 x
4
1 x4
5
can be written, for x 0 , as
x5
(3) (4)
1 4
x9
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
11. Which of the following is the simplified version of (1)
(2)
1 x
5
1 3 x
6
?
(3) x 2
1 x
(4) x 7
12. Which of the following represents the solution set to: 2 x 5 7 29 ? 2
29 2
(1) 5
(2) x 3 and 7
(3) x 2 and 8 (4) x 5 18
13. Which of the following represent the roots of the equation 2 x 2 6 x 1 0 ? (1) x 6 11
3 (3) x 2 11 2
3 11 (2) x 2 2
(4) 3 11
14. What are the zeroes of f x 6 x 2 31x 40 ? 31 543 12
(1) x
5 8 and 2 3
(3) x
(2) x
31 5 29 12
(4) x
3 5 and x 2 3
15. The larger root of the equation 3 x 2 5 x 1 0 is closest to (1) 1.43
(3) 2.57
(2) 1.87
(4) 3.19 COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
Free Response Questions
16. Given the function f x x 2 3 answer the following: (a) Graph the function on the grid shown.
(b) Explain how the graph of y x has been transformed into the graph of f x .
(c) What are the domain and range of f x ? Domain:
Range:
17. Solve the equation shown below algebraically. Be sure to check your solutions!!! x 2 19 2 x
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
18. Consider the function g x 2 x 2 5 x 12 . (a) Is x 1 a member of the natural domain of this function? Justify your yes/no response.
(b) Write an inequality that models the natural domain of this function. Explain how you arrived at your inequality.
(c) Algebraically solve the inequality you wrote in (b) to determine the natural domain of this function. Verify graphically and sketch a graph of g x on the axes below.
19. Jaylen and his brother Tyler are both in Algebra II and are debating a question about roots. Jaylen believes that taking the square root of a number and then the cube root of the result is the same as just taking the sixth root of the number. Tyler disagrees and believes that the combination of these two roots results in a fifth root. Who is correct and why?
20. Write
4
80x9 y16 in simplest radical form. Show how you arrived at your answer.
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
21. A projectile is fired vertically from an initial height of 8 feet with an initial velocity of 340 feet per second. Its height above the ground in feet can be modeled as a function of time by the equation h t 16t 2 340t 8
where t represents the seconds since fired
(a) Determine, algebraically, when the projectile hits the ground to the nearest tenth of a second.
(b) Write an inequality and solve it algebraically to determine all times at which the projectile is at or above 1,000 feet. Round all times to the nearest tenth of a second.
22. Solve the following system of equations algebraically. y x 10 1 y 2x 9
COMMON CORE ALGEBRA II, UNIT REVIEWS – UNIT #8 eMATHINSTRUCTION, RED HOOK, NY 12571, © 2015
