Additional Exercises 10.1 Form I Solving Quadratic Equations by the Square Root Property Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators. 1. x = 9 1.. x = 81. 3. x = 11 3.. x = 0. 5. 5x = 6 5. Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. If possible, simplify radicals or rationalize denominators. 6. x + x + = 9 6. 7. x 6x + 9 = 5 7. Use the Pythagorean Theorem to find the missing length in the right triangle. Express the answer in radical form, and simplify, if possible. 8. 8. 3 in in AE-31
Find the distance between each pair of points. Express answers in simplified radical form. 9. (1, ) (5, 7) 9. 10. (3, ) ( 6, 1) 10. 11. (, 8) ( 1, 5) 11. 1. (3, ) ( 5, 0) 1. 13. (8, ) ( 6, 3) 13. Solve each problem. 1. The formula F = 0.0x + 3 models the percentage of female 1. tenured faculty, F, at State University x years after 1980. According to the formula, in what year will the percentage of female tenured faculty reach 36.5? 15. The area of a circle is found by the equation A = πr. If the area 15. A of a certain circle is 5π square centimeters, find its radius r. AE-3
Additional Exercises 10.1 Form II Solving Quadratic Equations by the Square Root Property Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators. 1. x = 36 1.. x = 1. 3. 7x = 100 3.. ( x 3) = 36. 5. ( x + 5) = 0 5. Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. If possible, simplify radicals or rationalize denominators. 6. x + 0x + 100 = 19 6. 7. x + 10x + 5 = 7 7. Use the Pythagorean Theorem to find the missing length in the right triangle. Express the answer in radical form, and simplify, if possible. 8. 8. 15 in 0 in AE-33
Find the distance between each pair of points. Express answers in simplified radical form. 9. (, 5) (1, ) 9. 10. (, 6) ( 1, 3) 10. 11. (0, 8) (3, 5) 11. 1. (1, 1) ( 6, ) 1. 13. (, ) (5, 7) 13. Solve each problem. 1. Neglecting air resistance, the distance d, in feet, that an object 1. falls in t seconds is given by the equation d = 16t. If a window washer drops her bucket from the roof of a 56-foot building, how long will it take the bucket to hit the ground? 15. A square sheet of paper measures 8 centimeters on each side. 15. What is the length of the diagonal of this paper? AE-3
Additional Exercises 10.1 Form III Solving Quadratic Equations by the Square Root Property Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators. 1. y = 3 1.. x = 50. 3. 7x = 5 3.. (m 1) = 5. 5. (5x + ) = 10 5. Solve the quadratic equation by first factoring the perfect square trinomial on the left side. Then apply the square root property. If possible, simplify radicals or rationalize denominators. 6. x 6x + 9 = 6 6. 1 7. x x + = 7. Use the Pythagorean Theorem to find the missing length in the right triangle. Express the answer in radical form, and simplify, if possible. 8. 8. 19 m 11 m AE-35
Find the distance between each pair of points. Express answers in simplified radical form. 9. (1, 6) ( 3, ) 9. 10. (, ) ( 6, 0) 10. 11. (3, 5) (, 7) 11. 1. (1, 8) (3, 6) 1. 13. (, 3) (, 5) 13. Solve each problem. 1. A ladder that is 10 feet long is 6 feet from the base of a wall. 1. How far up the wall does the ladder reach? 15. A machine produces open boxes using square sheets of plastic. 15. The machine cuts equal-sized squares measuring inches on a side from each corner of the sheet, and then shapes the plastic into a open box by turning up the sides. If each box must have a volume of cubic inches, find the length of one side of the open box. AE-36
Additional Exercises 10. Form I Solving Quadratic Equations by Completing the Square Complete the square for each binomial. Then factor the resulting perfect square trinomial. 1. x + 10x 1.. x 16x. 3. x + 8x 3.. x x. 5. x + 1x 5. 6. x x 6. 7. x + x 7. 8. x 5x 8. 9. x + 18x 9. 10. x 7x 10. AE-37
Solve each quadratic equation by completing the square. 11. x + 1x + 7 = 0 11. 1. x x 8 = 0 1. 13. x + 3x 9 = 0 13. 1. x 1x = 35 1. 15. x x = 35 15. 16. x + 6x + 3 = 0 16. 17. 7x x = 0 17. 18. x 5x = 18. 19. x x 17 = 0 19. 0. x 9x + 9 = 0 0. AE-38
Additional Exercises 10. Form II Solving Quadratic Equations by Completing the Square Complete the square for each binomial. Then factor the resulting perfect square trinomial. 1. x 8x 1.. x + 0x. 3. x 9x 3.. x + 3x. 5. x 5x 5. 6. x + 11x 6. 7. x 18x 7. 8. x + 13x 8. 1 9. x x 9. 10. x x 10. AE-39
Solve each quadratic equation by completing the square. 11. x + x 1 = 0 11. 1. x + 1x + 17 = 0 1. 13. 3x = 7x 13. 1. x + x 3 = 0 1. 15. x x 13 = 0 15. 16. x + 8x = 0 16. 17. x 10x = 17. 18. x + 8x = 5 18. 19. x = 3 8x 19. 0. 6x = x + 0. AE-350
Additional Exercises 10. Form III Solving Quadratic Equations by Completing the Square Complete the square for each binomial. Then factor the resulting perfect square trinomial. 1. x 3x 1.. x + 5x. 3. x + 7x 3.. x + 9x. 5. x 15x 5. 1 6. x + x 6. 3 7. x x 7. 3 8. x + x 8. 7 1 9. x + x 9. AE-351
1 10. x x 10. Solve each quadratic equation by completing the square. 11. x + x 3 = 0 11. 1. x 6x = 16 1. 13. x x = 11 13. 1. x + 10x = 1. 15. x + 3x = 17 15. 16. 9x 1x = 0 16. 17. x = 6x + 5 17. 18. x + 1x = 15 18. 19. 6x + 11x = 10 19. 0. 7x + 1x = 1 0. AE-35
Additional Exercises 10.3 Form I The Quadratic Formula Solve the equation using the quadratic formula. Simplify irrational solutions, if possible. 1. x + x 15 = 0 1.. x 9x = 1. 3. 6x + x = 3.. x 6x + 3 = 0. 5. x + x 5 = 0 5. 6. x 1x + 30 = 0 6. 7. (x + 6) = 9 7. 8. x 3x 6 = 0 8. AE-353
9. 18x + 39x + 7 = 13 9. 10. x x = 7 10. 11. x + 3x = 0 11. 1. The formula P = 0.68x 0.0x + models the approximate 1. population P, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 6.16 thousand fish? 13. The formula N = x + x + 1 represents the number of house- 13. holds N, in thousands, in a certain city that have a computer x years after 1990. According to the formula, in what year were there 97 thousand households with computers in this city? 1. The hypotenuse of a right triangle measures 5 cm. One leg is 1. cm. shorter than the other leg. Find the measures of each leg and round to the nearest tenth if necessary. 15. An object is thrown upward from the top of a 160-foot building 15. with an initial velocity of 8 feet per second. The height h of the object after t seconds is given by the quadratic equation h = 16t + 8t + 160. When will the object hit the ground? Round to the nearest tenth of a second if necessary. AE-35
Additional Exercises 10.3 Form II The Quadratic Formula Solve the equation using the quadratic formula. Simplify irrational solutions, if possible. 1. x + x 1 = 0 1.. x + 6x + 1 = 0. 3. 3x = 1x 1 3.. x = 9 x. 5. x + 5x + 1 = 0 5. 6. x 8x = 1 6. 7. 3x 8x = 1 7. 8. x x = 0 8. AE-355
9. 3x 9x = 3 9. 10. x + 6x + 3 = 0 10. 11. x + 10x + 6 = 0 11. 1. The formula P = 0.68x 0.0x + models the approximate 1. population P, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 35.01 thousand fish? 13. The formula N = x + x + 1 represents the number of house- 13. holds N, in thousands, in a certain city that have a computer x years after 1990. According to the formula, in what year were there 1 thousand households with computers in this city? 1. The hypotenuse of a right triangle measures 15 feet long. One 1. leg of the triangle is 5 feet longer than the other leg. Find the perimeter of the triangle. 15. An object is thrown upward from the top of a 10-foot building 15. with an initial velocity of 8 feet per second. The height h of the object after t seconds is given by the quadratic equation h = 16t + 8t + 10. When will the object hit the ground? Round to the nearest tenth of a second if necessary. AE-356
Additional Exercises 10.3 Form III The Quadratic Formula Solve the quadratic equation by the square root property. If possible, simplify radicals or rationalize denominators. 1. x + 5x + 6 = 0 1.. x 5x = 0. 1 3. x x + = 0 3. 3 6. 0.01x + 0.06x 0.08 = 0. 5. x 8x + 1 = 0 5. 1 5 1 6. x x = 0 6. 3 6 7. x + x 7 = 0 7. 8. x + 1x = 5 8. AE-357
9. 6x = 1x 5 9. 10. x + 6x + 1 = 0 10. 1 1 1 11. x + x = 0 11. 1. The formula P = 0.68x 0.0x + models the approximate 1. population P, in thousands, for a species of fish in a local pond, x years after 1997. During what year will the population reach 5.168 thousand fish? 13. The formula N = x + x + 1 represents the number of house- 13. holds N, in thousands, in a certain city that have a computer x years after 1990. According to the formula, in what year were there 9 thousand households with computers in this city? 1. If the sides of a square are increased by 3 cm, its new area is 1. 100 cm. What did the sides of the square measure originally? 15. An object is thrown upward from the top of a 180-foot building 15. with an initial velocity of 8 feet per second. The height h of the object after t seconds is given by the quadratic equation h = 16t + 8t + 180. When will the object hit the ground? Round to the nearest tenth of a second if necessary. AE-358
Express each number in terms of i. Additional Exercises 10. Form I Imaginary Numbers as Solutions of Quadratic Equations 1. 9 1.. 6. 3. 900 3.. 0. 5. 80 5. 6. 300 6. 7. 8 + 11 7. 8. 5 8. 9. 7 + 6 9. AE-359
Solve the quadratic equation using the square root property. Express complex solutions in form. 10. ( + ) = 16 a + bi x 10. 11. ( + 5) = 100 x 11. 1. ( 6) = 6 x 1. 13. ( 8) = 9 x 13. 1. ( ) = 1 x 1. Solve the quadratic equation using the quadratic formula. Express the complex solutions in a + bi form. 15. x 8x + 5 = 0 15. 16. 3x + 30x + 10 = 0 16. 17. x + x + 10 = 0 17. 18. x + 13 = x 18. 19. x x = 9 19. 0. x + x = 7 0. AE-360
Express each number in terms of i. Additional Exercises 10. Form II Imaginary Numbers as Solutions of Quadratic Equations 1. 5 1.. 7. 3. 3.. 10. 5. 600 5. 6. 50 6. 7. 5 + 8 7. 8. 1 6 8. 9. 11 3 9. AE-361
Solve the quadratic equation using the square root property. Express complex solutions in form. 10. ( 15) = 0 a + bi x 10. 11. ( 10) = 1 x 11. 1. ( + 3) = 13 y 1. 13. ( + 1) = 3 x 13. 1. ( 11) = 50 x 1. Solve the quadratic equation using the quadratic formula. Express the complex solutions in a + bi form. 15. x + 9 = 0 15. 16. x x = 16. 17. x x = 5 17. 18. 3r = r 18. 19. x x = 3 19. 0. y y = 10 0. AE-36
Express each number in terms of i. Additional Exercises 10. Form III Imaginary Numbers as Solutions of Quadratic Equations 1. 98 1.. 150. 3. 80 3.. 13. 5. 3 5. 6. 70 6. 7. 1 + 8 7. 8. 19 50 8. 9. + 17 9. AE-363
Solve the quadratic equation using the square root property. Express complex solutions in form. 10. ( 5 + 3) = 6 a + bi x 10. 11. ( + 1) = 7 x 11. 1. ( 3 ) = 1 x 1. 13. ( + 5) = 11 x 13. 1. ( + 1) = 38 y 1. Solve the quadratic equation using the quadratic formula. Express the complex solutions in a + bi form. 15. 3x x = 10 15. 16. x 10x = 7 16. 17. x + x + 8 = 0 17. 18. x + 7x 9 = 0 18. 19. x x = 1 3 19. 0. x + x + 3 = 0 0. AE-36
Additional Exercises 10.5 Form I Graphs of Quadratic Equations Determine if the parabola whose equation is given opens upward or downward. 1. y = x + x 6 1.. y = x + x. Find the two x- intercepts for the parabola whose equation is given. Round irrational answers to the nearest tenth, if necessary. 3. y = x + x 3 3.. y = x + 17x 7. 5. y = x + 6x 56 5. Find the y-intercept for the parabola whose equation is given. 6. y = x x 6. 7. y = 3x x + 1 7. 8. y = x 7x 8 8. Find the vertex for the parabola whose equation is given. 9. y = x + 7 9. 10. y = x 8x 10. 11. y = 3x + 6x + 6 11. AE-365
Graph the parabola whose equation is given. 1. y = x 6x + 8 1. 6 Y X -6 - - 0-6 - -6 13. y = x + x + 3 13. 6-6 - - 0-6 - -6 Y X 1. y = x + 1 1. Y X -6 - - 0-6 - -6 Solve. 15. The cost in millions of dollars for a company to manufacture 15. x thousand automobiles is given by the function C ( x) = x 0x + 5. Find the number of automobiles that must be produced to minimize the cost. 6 AE-366
Additional Exercises 10.5 Form II Graphs of Quadratic Equations Determine if the parabola whose equation is given opens upward or downward. 1. y = 3x + 5 1.. y = x x + 7. Find the x- intercept for the parabola whose equation is given. Round irrational answer to the nearest tenth, if necessary. 3. y = x + 18x 3.. y = x + 3x 7. 5. y = x x + 5. Find the y- intercept for the parabola whose equation is given. 6. y = x 9x + 6 6. 7. 1 3 y = x + x 7. 8. y = 5x 9 8. Find the vertex for the parabola whose equation is given. 9. y = 3 x + x 9. 10. y = x + 1 10. 11. y = x x 1 11. AE-367
Graph the parabola whose equation is given. 1. y = x 8x + 15 1. 6 Y X -6 - - 0-6 - -6 13. y = 6x 3x + 1 13. 6-6 - - 0-6 - -6 Y X 1. 1 x y = 1. 6 Y X -6 - - 0-6 - -6 Solve. 15. A projectile is fired from a cliff 00 feet above the water. 15. The height h of the projectile above the water is given by 3x h = + x + 00, where x is the horizontal distance (0) of the projectile from the base of the cliff. Find the maximum height of the projectile. AE-368
Additional Exercises 10.5 Form III Graphs of Quadratic Equations Determine if the parabola whose equation is given opens upward or downward. 1. 3 5 1 y = x x + 1. 7. y = 0.7x + 0.9x 1.. Find the x- intercept for the parabola whose equation is given. Round irrational answer to the nearest tenth, if necessary. 3. y = x 3.. y = x x + 7. 5. y = x 5x + 1 5. Find the y- intercept for the parabola whose equation is given. 6. y = 0.07x 0.9x + 0. 15 6. 7. 5 1 3 y = x x + 7. 8 7 8. y = 19x + 15x 8. Find the vertex for the parabola whose equation is given. 9. y = x 3x 9. 10. y = x + 7x + 7 10. 11. y = x + x 11. AE-369
Graph the parabola whose equation is given. 1. y = 5x 10x + 1. 6 Y X -6 - - 0-6 - -6 13. y = x x 13. 6-6 - - 0-6 - -6 Y X 1. y = x 3x 1. 6-6 - - 0-6 - -6 Solve. 15. The profit that a vendor makes per day by selling x pretzels 15. is given by the function P ( x) = 0.00x + 1.6x 350. Find the number of pretzels that must be sold to maximize profit. Y X AE-370
Additional Exercises 10.6 Form I Introduction to Functions Decide whether the relation defines a function. 1. {( 3, 3), (3, 9), (, ), (9, 3), (11, 7)} 1.. {(, 7), ( 1, ), (3, 5), (3, 9)}. 3. {(, ), ( 1, 8), (1, 5), (6, 6)} 3.. {( 6, 9), ( 6, 1), (, 6), (3, 8), (8, 9)}. Find the domain and range. 5. {( 6, 6), (, 9), (10, 5)} 5. 6. {(1, 6), ( 1, 7), (1, 5)} 6. 7. {(3, 1), ( 1, 6), (, 3) 7. 8. {( 1, ), (9, ), ( 3, 7)} 8. Evaluate the function at the given value. 9. Find f (0) when f ( x) = x 6 9. 10. Find f (3) when f ( x) = x 5x + 10. 11. Find h (9) when h ( x) = x 8 11. 1. Find f (3) when f ( x) = x 5x 1. AE-371
13. Find f () when f ( t) = t + 117 9 13. 1. Find f ( 5) when r f ( r) = 1. r Use the vertical line test to determine if the graph is a function of x in y. 15. Y 6 15. -6 - - 0-6 - -6 X 16. Y 6 16. -6 - - 0-6 - -6 X 17. Y 6 17. -6 - - 0-6 - -6 X AE-37
Solve. 18. The monthly cost of a certain long distance service is 18. given by the linear function C ( t) = 0.07t + 3. 95 where C(t) is in dollars and t is the amount of time in minutes called in a month. Find the cost of calling long distance for 180 minutes in a month. 19. A rocket is stopped 7 feet from a satellite when it begins 19. accelerating away from the satellite at a constant rate of 8 feet per second. The distance between the rocket and the satellite is given by the polynomial P ( t) = t + 7. Find the distance between the rocket and the satellite 11 seconds after the rocket started moving. 0. The function W ( g) = 0.5g 0.06g + 7. models the average 0. weight in ounces for a mouse who is fed g grams per day of a special food. Use the function to find and interpret W(5). Round the answer to the nearest tenth. AE-373
Additional Exercises 10.6 Form II Introduction to Functions Decide whether the relation defines a function. 1. {(, 1), (3, 7), (8, 5), (6, 8), (0, 5)} 1.. {(1, ), (1, 3), (1, ), (1, 5)}. 3. {( 3, 5), (6, 5), (, 5), (1, 5)} 3.. {(3, ), (5, 1), (6, 7), (0, ), ( 6, 5)}. Find the domain and range. 5. {(1, 5), (0, 6), ( 5, )} 5. 6. {( 5, 3), (, 8), (1, 0)} 6. 7. {(1, 1), (, ), (3, 3) 7. 8. {(8, 5), ( 6, 5), (0, 5)} 8. Evaluate the function at the given value. 9. Find f (6) when f ( x) = x 6 9. 10. Find f ( 1) when f ( x) = x 5x + 10. 11. Find h () when h ( x) = x 8 11. 1. Find f (0) when f ( x) = x 5x 1. AE-37
13. Find f ( 17) when f ( t) = t + 117 9 13. 1. Find f (1) when r f ( r) = 1. r Use the vertical line test to determine if the graph is a function of x in y. 15. Y 6 15. -6 - - 0-6 - -6 X 16. Y 6 16. -6 - - 0-6 - -6 X 17. Y 6 17. -6 - - 0-6 - -6 X AE-375
Solve. 18. The monthly cost of a certain long distance service is 18. given by the linear function C ( t) = 0.07t + 3. 95 where C(t) is in dollars and t is the amount of time in minutes called in a month. Find the cost of calling long distance for 10 minutes in a month. 19. A rocket is stopped 7 feet from a satellite when it begins 19. accelerating away from the satellite at a constant rate of 8 feet per second. The distance between the rocket and the satellite is given by the polynomial P ( t) = t + 7. Find the distance between the rocket and the satellite 1 seconds after the rocket started moving. 0. The function W ( g) = 0.5g 0.06g + 7. models the average 0. weight in ounces for a mouse who is fed g grams per day of a special food. Use the function to find and interpret W(18). Round the answer to the nearest tenth. AE-376
Decide whether the relation defines a function. Additional Exercises 10.6 Form III Introduction to Functions 1. {(1, ), (, 0), ( 3, 5), (5, 8), (6, 7)} 1.. {(3, 3), (, ), (5, 5), (6, 6)}. 3. {( 1, 8), ( 1, ), ( 1, 6), ( 1, 8)} 3.. {(6, ), (9, ), ( 8, ), (, )}. Find the domain and range. 5. {(8, 1), ( 3, 6), (5, 0)} 5. 6. {(, ), (7, 1), (8, 9)} 6. 7. {(5, 5), (, ), (6, 6) 7. 8. {(9, 3), (5, ), (0, 1)} 8. Evaluate the function at the given value. 9. Find f ( 5) when f ( x) = x 6 9. 10. Find f ( ) when f ( x) = x 5x + 10. 11. Find h ( ) when h ( x) = x 8 11. 1. Find f ( ) when f ( x) = x 5x 1. AE-377
13. Find f (7) when f ( t) = t + 117 9 13. 1. Find f (6) when r f ( r) = 1. r Use the vertical line test to determine if the graph is a function of x in y. 15. Y 6 15. -6 - - 0-6 - -6 X 16. Y 6 16. -6 - - 0-6 - -6 X 17. 17. AE-378
Solve. 18. The monthly cost of a certain long distance service is 18. given by the linear function C ( t) = 0.07t + 3. 95 where C(t) is in dollars and t is the amount of time in minutes called in a month. Find the cost of calling long distance for 35 minutes in a month. 19. A rocket is stopped 7 feet from a satellite when it begins 19. accelerating away from the satellite at a constant rate of 8 feet per second. The distance between the rocket and the satellite is given by the polynomial P ( t) = t + 7. Find the distance between the rocket and the satellite 18 seconds after the rocket started moving. 0. The function W ( g) = 0.5g 0.06g + 7. models the average 0. weight in ounces for a mouse who is fed g grams per day of a special food. Use the function to find and interpret W(0). Round the answer to the nearest tenth. AE-379