45. Find the discriminant and the solution of each equation in parts (a)–(c). If necessary, round to the nearest hundredth.
    1. x 2 − 6 x + 5 = 0 x squared , minus 6 . x plus 5 equals 0
    2. x 2 + x − 20 = 0 x squared , plus , x minus 20 equals 0
    3. 2 x 2 − 7 x − 3 = 0 2 x squared , minus 7 x minus 3 equals 0
    4. Reasoning When the discriminant is a perfect square, are the solutions rational or irrational? Explain.

C Challenge

46. Reasoning The solutions of any quadratic equation a x 2 + b x + c = 0 eh x squared , plus b x plus c equals 0  are − b + b 2 − 4 a c 2 a fraction negative b plus . square root of b squared , minus 4 eh c end root , over 2 eh end fraction  and − b − b 2 − 4 a c 2 a , fraction negative b minus . square root of b squared , minus 4 eh c end root , over 2 eh end fraction . comma
    1. Find a formula for the sum of the solutions.
    2. One solution of 2 x 2 + 3 x − 104 = 0 2 x squared , plus 3 x minus 104 equals 0  is − 8 . negative 8 .  Use the formula you found in part (a) to find the second solution.

Reasoning For each condition given, tell whether a x 2 + b x + c = 0 eh x squared , plus b x plus c equals 0  will always, sometimes, or never have two solutions.

47. b 2 < 4 a c b squared , less than 4 . eh c
48. b 2 = 0 b squared , equals 0
49. a c < 0 eh c less than 0

Standardized Test Prep

SAT/ACT

50. What are the approximate solutions of the equation x 2 − 7 x + 3 = 0 ? x squared , minus 7 . x plus 3 equals 0 question mark
    1. − 6.54 , 0.46 negative , 6.54 , comma , 0.46
    2. − 6.54 , − 0.46 negative , 6.54 , comma negative , 0.46
    3. − 0.46 , 6.54 negative , 0.46 , comma , 6.54
    4. 0.46, 6.54
51. Which of the following relations is a function?
    6. { ( 1 , 2 ) , ( 3 , 5 ) , ( 1 , 4 ) , ( 2 , 3 ) } the set open 1 comma 2 close comma open 3 comma 5 close comma open 1 comma 4 close comma open 2 comma 3 close end set
    7. { ( − 5 , 6 ) , ( 0 , 9 ) , ( − 1 , 2 ) , ( 0 , 6 ) } the set open negative 5 comma 6 close comma open 0 comma 9 close comma open negative 1 comma 2 close comma open 0 comma 6 close end set
    8. { ( 8 , 2 ) , ( 6 , 3 ) , ( 6 , 11 ) , ( − 8 , 2 ) } the set open 8 comma 2 close comma open 6 comma 3 close comma open 6 comma 11 close comma open negative 8 comma 2 close end set
    9. { ( − 1 , 3 ) , ( 7 , 3 ) , ( − 7 , 2 ) , ( 4 , 5 ) } the set open negative 1 comma 3 close comma open 7 comma 3 close comma open negative 7 comma 2 close comma open 4 comma 5 close end set
52. What equation do you get when you solve 3 a − b = 2 c  for  b ? 3 eh minus b equals 2 c , for , b question mark
    1. b = − 3 a + 2 c b equals negative 3 eh plus 2 c
    2. b = 3 a − 2 c b equals 3 eh minus 2 c
    3. b = 3 a + 2 c b equals 3 eh plus 2 c
    4. b = − 3 a − 2 c b equals negative 3 eh minus 2 c
53. What are the approximate solutions of the equation 1 3 x 2 − 5 4 x + 1 = 0 ? 1 third , x squared , minus , 5 fourths , x plus 1 equals 0 question mark  Use a graphing calculator.
    6. 1.07, 2.77
    7. 1.16, 2.59
    8. 0.87, 10.38
    9. 0.19, 16.01

Short Response

54. Suppose the line through points (n, 6) and (1, 2) is parallel to the graph of 2 x + y = 3 . 2 x plus y equals 3 .  Find the value of n. Show your work.

Mixed Review

See Lesson 9-5.

Solve each equation by completing the square.

55. s 2 − 10 s + 13 = 0 s squared , minus 10 . s plus 13 equals 0
56. m 2 + 3 m = − 2 m squared , plus 3 . m equals negative 2
57. 3 w 2 + 18 w − 1 = 0 3 w squared , plus 18 w minus 1 equals 0

Get Ready! To prepare for Lesson 9-7, do Exercises 58–61.

See Lesson 7-6.

Graph each function.

58. y = 2 x y equals , 2 to the x
59. y = 3 x y equals , 3 to the x
60. y = ( 1 3 ) x y equals . open , 1 third , close to the x
61. y = ( 1 2 ) x y equals . open , 1 half , close to the x

Table of Contents