The height (in feet) that you can throw the grappling hook is given by the function y = -16t2 + 48t + 5. Can you throw the hook high enough to reach t...
1. You are shot out of a cannon at the fair. The 1 equation y (x 2)(x 28) models your flight 5 path, where y is the height (in feet) above the ground and x is the horizontal distance traveled (in feet). Which of the following statements are true? a. You reach a maximum height of 45 feet. b. You will land 11.2 feet from the cannon. c. The barrel of the cannon is about 11 feet above the ground. d. At a point 13 feet from the cannon, you begin to descend. 2. Which of the following statements are true? 25 5 a. b. (2 5i) (3 4i) 5 9i 2 c. 6i 2 6 d. The solutions of x 2 21 38 are x i
12. (x 5 ) 4 (x 9) (x 1) 28 2
13. 6x x 2 10 Solve the system. 14. y 6x 3x 2
3x 2 12 12x y 15. y x 2 3
11 x 2 y 17 .
16. x 2 y 2 81
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3. Which statements about the quadratic function f(x) x 2 20x 38 are true? a. To complete the square, add 10 to each side of the equation. b. The vertex form is f(x) (x 10) 2 138 . c. The vertex of the graph is (10, 138). d. The maximum value is 138 .
17. y 12x 14 2x 2
3x 2 18x 26 y 0 Find the zero(s) of the function.
Solve the equation.
18. g(x) x 2 9x 8
4. 3 (x 2 ) 8 5 2
19. h(x) 2x 2 4x 70
5. x 2 53 98 20. f (x )
6. x 4x 4 25 2
1 2 x 72 3
Find the square root of the number.
7. x 2 4x 11 0
21. 2 16
8. x(x 9) 7
Find the values of x and y that satisfy the equation.
9. 3x 2 15x 186 0 10. 5x(x 2) 130
22. 4 7yi
1
1 x 3i 8
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IA 35. You have a garden that measures 13 feet by 16 feet. You want to put a sidewalk around the garden but are not sure how wide to make it. Determine how wide the sidewalk should be when the total area of the garden and sidewalk is 460 square feet. Justify your answer.
Perform the operation. Write the answer in standard form. 23. 6 (8 17i) 16i 24. 4i(9 9i)
36. Find the discriminant of the quadratic equation 4x 2 6x 25 0 and describe the number and type of solutions of the equation.
25. (1 4i) (9 4i) 26. Find the value of c that makes s 2 13s c a perfect square trinomial. Then write the expression as the square of a binomial.
37. Find a possible pair of integer values for a and c so that the equation 5x c ax 2 has two imaginary solutions. Then write the equation.
27. Graph y (x 3 ) 3. 2
38. During World War I, mortars were launched upward with an initial velocity of 154 feet per second from trenches that were 6 feet deep. Write an equation that represents the height (in feet) above the ground of a mortar t seconds after it has been launched. How long does the mortar take to hit the ground? Round your answer to the nearest tenth of a second.
Graph the system of quadratic inequalities. 28.
y x 2 2x 2 y x 2 3x 2 Solve the inequality. Round decimal answers to the nearest hundredth.
39. A rectangular playground must have a perimeter of 460 feet and an area of at least 8600 feet. Describe the possible lengths of the playground.
29. x 2 7x –10 30. x 2 9x –18
40. You and your friends design a container that prevents tomatoes from exploding when dropped from a height of 80 feet.
31. x 2x 9 2
32. x 2 9x 11
a. Write a function that gives the height h (in feet) of the container after t seconds. How long does it take for the container to hit the ground?
33. An amusement park has 24,000 visitors per day when it charges $30 per person. For each $1 increase in price, the park loses about 500 visitors. How much should the park charge to maximize daily revenue? What is the maximum daily revenue?
b. Find and interpret h(0.5) – h(1).
34. You and a friend are hiking in the mountains. You want to climb to a ledge that is 150 feet above you. The height (in feet) that you can throw the grappling hook is given by the function y 16t 2 48t 5 . Can you throw the hook high enough to reach the ledge? Explain.
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ID: A
CC Algebra 2H: Chapter 3 Review Answer Section 1. A, C, D 2. C, D 3. B, C
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5. x 3i 5 6. x 7 and x 3 7. x 2 i 8. x
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5 i 223 2 x 1 5i x 6 3i x 4 and x 5 no real solution ÊÁ 2,0ˆ˜ and ÊÁ 1,3 ˆ˜ Ë ¯ Ë ¯
9. x 10. 11. 12. 13. 14.
15. ÊÁË 2,7ˆ˜¯ and ÊÁË 2,7 ˆ˜¯ 16. ÊÁË 0,9 ˆ˜¯
17. ÊÁË 2,2ˆ˜¯ and ÊÁË 4,2 ˆ˜¯ 18. x 1 and x 8 19. x 7 and x 5 20. x 6i 21. 8i
5 x 2 6 x 3 about x 2.16 or x 4.16 about x 10.09 or x 1.09 $39; $760,500 no ; The maximum height you can throw the grappling hook is 41 feet. 3.5 ft; (2x 13) (2x 16) 460 4x 2 58x 252 0 x
58
58 2 4(4)(252) 2(4)
x 18 and x 3.5 Reject the negative solution of –18 because the width cannot be negative. 36. –364; two imaginary solutions 37. Sample answer: a = –4 and c = –24; 4x 2 5x 24 0 38. y 16t 2 154t 6 ; about 9.6 sec 39. at least 47 ft and at most 183 ft 40. a. h (t ) 16t 2 80; about 2.2 sec b. 12; The container fell 12 feet between 0.5 and 1 seconds.
