SECONDARY 2H ~ UNIT 5 (Intro to Quadratics) Assignments from your Student Workbook are labeled WB Those from your hardbound Student Resource Book are labeled RB. Do all work from the Student Resource Book (RB) on a separate piece of paper. 5.1 Expressions, Words, and Quadratics (3.1.1, 3.1.2) Identify the terms, coefficients, and constant of the following expressions: 1. 16x 2 12x + 20 2. 30x 2 18x + 72 Simplify the expressions and classify each as a monomial, binomial, or trinomial: 3. 3x 2 + 2(5 x 2 ) 8(x 2 + 9) 4. 5x + 4(5x x) 2x(6) For the following problems, write an algebraic expression and simplify if possible: 5. three decreased by twice a number 6. five times a number decreased by three 7. fourteen decreased by the square of a number 8. twice the sum of a number and 11 9. four times the sum of a number and its square 10. the product of the square of a number and five 11. the sum of 7 and three times a number 12. the square of the sum of a number and 13 13. the product of 7 and the square of x, increased by the difference of 5 and x 2 14. half the sum of 12 and x 2 decreased by one-third x 15. the product of 9 and x, decreased by the sum of 8 and the square of x 16. double the sum of 2 and x increased by one-half x 2 Simplify the expressions and determine whether each is a quadratic: 17. 3x(x + 14) 18. 20x(4 5x) + 3(x 8) 19. (x 1) 2 + 10 20. 12x(x 2 4x) 2(3 + x) 21. (x + 4)(5x 11) 22. (2x 2 + 9)(x 2) 23. (x + 4)(x + 1)(x 1) Write a quadratic expression for the following: 24. contains 2 terms, a coefficient of 7 and a constant of 10 25. contains 3 terms, coefficients of -1 and 1, and a constant of 52 Continued on next page.
Write the following quadratic expressions in standard form and identify a, b and c 26. (3x + 5)(4x 1) 27. 3x(2x + 8) + (x 3)(x + 10) 28. (x 2)(x + 3) (x 4)(2x + 5) 5.2 Quadratic Graphs (2.1.1) WB: Page 13 #1-7: Without your calculator state whether the graph opens up or down and find the y-intercept. Then use your calculator to list the vertex and state whether it is a maximum or minimum, give the x-intercepts and state where the graph is increasing or decreasing. #8 10: Without the calculator state whether the graph has a maximum or minimum and find the y-intercept. Then use your calculator to find the max or min and the x-intercepts. 5.3 Domain and story problems (2.1.2, 2.2.2) WB: Page 23 #1 10 Show work on 2b, skip 2c. #4-10 graph on your calculator, you do not need to draw on paper. On #5 do not answer the last question. Page 43 #1-4, 8-10 On #8 10 show what you found first, in order to answer the question, then answer in a sentence 5.4 Solve by factoring (3.2.2) WB: Page 43 # 1-10 AND do the following: Solve each equation by factoring: 1. x 2 x = 12 2. y 2 5y = 0 3. 9x 2 + 16 = 24x 4. 4x 2 11x 3 = 0 5. 4y 2 = 25 6. 12m 2 + 25m + 12 = 0 7. 18n 2 = 15 + 3n 8. z 2 z = 0 9. 2x 2 18 = 0 10. r 2 = 3r + 4 Continued on next page.
Write a quadratic equation that has the given zeros: 11. x = 6, -9 12. x = 5, -1 13. x = 2, 5 8 15. x = -4, 2 3 16. x = 4 3, 1 6 14. x = 2 5, 2 5 5.5 Solve by Square Roots WB: Page 33 #1-10 RB: page U3-25 #1 6, 8-10 ANSWERS FOR ASSIGNMENTS: Remember: this is only to check your answers ~ all work must be shown, or no credit will be given!! (Also we re only human, so there may be mistakes! ) 5.1 answers: 1. terms: 16x 2, 12x, 20; coefficients: 16, 12; constant: 20 2. terms: 30x 2, 18x, 72; coefficients: 30, 18; constant: 72 3. 7x 2 62, binomial 4. 9x, monomial 5. 3 2x 6. 5x 3 7. 14 - x 2 8. 2(x + 11) 9. 4(x + x 2 ) 10. 5x 2 11. 7 + 3x 12. (x + 13) 2 13. 6x 2 + 5 14. 1 2 x2 1 3 x + 6 15. x 2 + 9x 8 16. 1 2 x2 + 2x + 4 17. 3x 2 42x, Quadratic 18. 100x 2 + 83x 24, quadratic 19. x 2 2x + 11, Quadratic 20. 12x 3 48x 2 2x 6, not quadratic 21. 5x 2 + 9x 44, Quadratic 22. 2x 3 4x 2 + 9x 18, not quadratic 23. x 3 + 4x 2 x 4, not quadratic 24. 7x 2 + 10 25. x 2 + x + 52 26. 12x 2 + 17x 5, a=12, b=17, c= -5 27. 7x 2 + 31x 30, a=7, b=31, c= -30 28. x 2 + 4x + 14, a = -1, b = 4, c = 14
5.2 answers: WB: Page 97 1. opens up, y-int. (0, 5), vertex (-3, -4), a minimum, x-int. (-1, 0), (-5, 0), incr. x > -3, decr. x< -3 2. opens up, y-int. (0, -15), vertex (-1, -16), a minimum, x-int. (3, 0), (-5, 0), incr. x> -1, decr. x< -1 3. opens down, y-int. (0, -9), vertex (5, 16), a maximum, x-int. (1, 0), (9, 0), incr. x < 5, decr. x >5 4. opens down, y-int. (0, 0), vertex (-2, 4), a maximum, x-int. (-4, 0), (0, 0), incr. x < -2, decr. x > -2 5. opens up, y-int. (0, -12), vertex (2, -16),a minimum, x-int. (-2, 0), (6, 0), incr. x > 2, decr. x < 2 6. opens up, y-int. (0, 0), vertex (-2, -2), a minimum, x-int. (-4, 0), (0, 0), incr. x > -2, decr. x < -2 7. opens down, y-int. (0, -3), vertex (-2, 1), a maximum, x-int. (-3, 0), (-1, 0), incr. x< -2, decr. x > -2 8. has maximum, y-int. (0, 0), max. (6, 18), x-int. (0, 0), (12, 0) 9. has maximum, y-int. (0, 16), max (0.75, 25), x-int. (-.5, 0), (2, 0) 10. has maximum, y-int. (0, 16), max (3, 25), x-int. (-2, 0), (8, 0) 5.3 answers: WB: Pg. 107 1a. (0, 8) 1b. (3, -1) 1c. minimum 2a. (-2, 0), (4, 0) 2b. (0, 4) 2d. (1, 4.5) 3a. (1, 10), 3b. maximum 4. vertex: (7, -9) The lowest the bird will go is 9 feet below the surface of the lake, after 7 seconds of flight. 5. x-int. (-2, 0), (40, 0) the x-intercepts are the times when the missile is on the ground (height of 0). The x-int of -2 does not make sense because time cannot be negative, so the missile is back on the ground after 40 seconds. 6. x-int. (-1, 0) and (2, 0); the x-intercepts are the times when the snowboarder is on the ground. The x-intercept -1 does not make sense because time cannot be negative. The stunt lasted 2 seconds. 7. vertex: (3, 25) The paper airplane will reach its maximum height of 25 feet after going 3 feet horizontally. 8. vertex: (1, 16) The golf ball will reach its maximum height of 16 feet 1 second after being hit. 9. x-int. (15, 0) and (-5, 0); The x-intercepts show the number of dollars of price increase that would result in 0 revenue. The x-int or -5 does not make sense because you would not have a negative price increase. A price increase of $15 would result in 0 revenue. The revenue is maximized when x=5. 10. vertex: (7, 289) The maximum revenue is $289 and it will occur when the price is reduced by $7. WB: page 127 #1-4 all answers are all real numbers 8. The ball is in the air just less than 3.9 seconds 9. The golf ball hits the ground after 9.4 seconds 10. Domain: 8.67 x 28.83 (tell where this is from). Profits will be maximized when x = $18.75
5.4 answers: WB: Page 289 1. 8a(a 5) 2. (y 3)(y 4) 3. (2z + 3) 2 4. x = 15, 5 5. r = 0, 40 6. x = 4, 1 7. x = 3, 1 2 8. Tickets can be sold for $0 or $20 for an income of $0. 9. The width is (x 2) feet. 10. The base of the triangle is 5 inches. Packet: 1. x = 3, 4 2. y = 0, 5 3. x = 4 3 4. x = 1 4, 3 5. y = 5 2, 5 2 6. m = 3 4, 4 3 7. n = 5, 1 8. z = 0, 1 6 9. x = 3, 3 10. r = 1, 4 11. x 2 + 3x 54 = 0 12. x 2 4x 5 = 0 13. 8x 2 21x + 10 = 0 14. 25x 2 4 = 0 15. 3x 2 + 14x + 8 = 0 16. 18x 2 21x 4 = 0 5.5 answers: WB: Page 279 1. x = ±9 2. x = ±5i 3. x = ±3 4. x = 4, 2 5. x = 3 ± 3i 6. x = 15, 25 2 2 7. c b a must be positive and a perfect square 8. The length of one side of the square is 2 10 cm. 9. The radius of the circle is 4.37 mm. 10. The side length of the cube is 10 3 RB: page U3-25 3 inches. 1. x = ±2 2. x = ±2i 3. x = ±2i 2 4. x = 4 ± 2 10 5. x = 6 6. x = 5 ± 7 8. The length of one side of the square is 7 in. 9. The radius of the circle is 2 5 10. The radius of the sphere is 1.26 ft.
REVIEW answers: 1. Terms: 13x 2, 7x, 17, Coefficients: 13 and 7, Constant: 17 2. 4x 2 + 42, binomial 3. Yes, x 2 + 7x + 13. 4. No, 2x 3 + 3x 2 7x + 3 5. 3x 2 + 3x + 12 6. x 2 + x + 11 7. m = 4, 1 8. b = 1, 2 9. m = 6 10. c = 0, 7 2 11. n = 8, 2 12. x = 8, 4 13. width = (a 2)feet 5 14. The base equals 4 inches. 15. 35x 2 + 4x 4 = 0 16. a = ±8 17. k = ±10 18. x = 4 ± 2i 19. p = 3 ± 4 2 20. x = ± 6 7 21. r = 2 7 or 5.29 inches 22. opens up; y-int (0, -7); vertex (-3, -16); minimum; x-ints (-7, 0), (1, 0); incr. x > -3, decr. x< -3 23. opens down; y-int (0, 0); vertex (-2, 2); maximum; x-ints (0, 0), (-4, 0); incr. x <-2, decr. x > -2 24. opens down: y-int (0, -16); vertex (-3, 2); maximum; x-ints (-4, 0), (-2, 0); incr. x<-3, decr. x > -3 25. maximum; y-int (0, 7); maximum (3, 16); x-ints (-1, 0), (7, 0) 26. Domain: x = all real numbers 27. Vertex (5, 1); The butterfly is one foot above the ground after 5 seconds in flight. 28. Vertex (1, 52); The diver is 52 feet above the water one second into his dive. 29. x-ints (50, 0) (-2, 0); The x-intercepts represent the number of widgets made that will result in a revenue of $0. The x-intercept at (-2, 0) does not make sense in context, since they can t produce a negative number of widgets. The revenue is maximized at 24 widgets. 30. 20 seconds 31. Answers will vary 32. Answers will vary 33. No. A quadratic can have 1 real solution, 2 real solutions, or 2 non-real solutions.