Algebra 1 Common Core Student Edition, Grade 8-9

4. y
   X
   -l I— 0! L

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1 \

/'I \

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5. If a > 0, the graph opens upward and the vertex is a
   minimum. If a < 0, the graph opens downward and the
   vertex is a maximum. The greater the value of |a |, the
   narrower the parabola is. The axis of symmetry is the line
   x = The x-coordinate of the vertex is - ^. The
   y-intercept of the parabola is c. 6. First graph the vertex
   and then graph the y-intercept. Reflect the y-intercept
   over the axis of symmetry to get a third point. Then sketch
   the parabola through these three points.
   Ex e r c i se s 7. x = 0; (0, 3) 9. x = - 1 ; ( -1, - 3 )


6. x = 1.5; (1.5, -4 .7 5 ) 13. x = 0.3; (0.3, 2.45)


7. x=-0.5; (-0.5,-6.5) 17. B 19. A


8. 25ft; 625 ft2; 0 < A < 6 2 5

29a. (-1, 19) b. (-2 ,-5 ) 31. $50

33. The value of b is - 6 , so

-S - - ( 2 ^) “ “(^f) “ -3 35a'°'4s b-N°'the

ball does n o t sta rt a t height 0 m.

Lesson 9-3 pp. 56 1-5 66

Go t It? l a. ±4 b. no solution c. 0 2a. ±6 b. no
solution c. 0 3a. 7.9 ft b. The solutions of the equation
in Problem 3 are irrational numbers, which are difficult to
approximate on a graph.
Lesso n Ch eck 1. ±5 2. ±2 3. ±12 4. ±15 5. The
zeros of a function are the x-intercepts of the function.
Example: y = x 2 - 25 has zeros ± 5. 6. Answers will
vary. Sample: When an equation has noninteger solutions,

it is almost always easier to use square roots to find its

solutions. 7. a and c have opposite signs; c = 0; a and c

have the same sign.

Ex e r c i se s 9. no solution 11. ±2 13. ±3 15.0

17. no solution 19. ±3 21. ±18 23.0 25. ± |


18. ±2 29. ±4 31. ±3 33. Let x = length of side
    of a square, then x 2 = 75; 8.7 ft 35. 7.1 ft 37. 0 39. 1


19. n>0;n = 0;n<0 43. no solution 45. ±g


20. ±0.4 49. 144 51. When you subtract 100 from
    each side, you get x 2 = - 100 , which has no
    solution. 53.6.3 ft 55a. = 6(A2)A2 - 24
    b. ± 2 ; the solution(s) of the quadratic equation is (are)
    the x-value(s) in column A that make(s) the value in
    column B equal 0. c. Answers may vary. Sample: Find
    each instance of a sign change in column B. The
    solution(s) lie(s) between the corresponding x-values
    in column A. 57. 28 cm
    Lesson 9-4

Go t It? 1a

pp. 568-572

-1, 5 b. -§, 4 c. -j, -14 d. j, f

2a. -2, 7 b. -5, 4 c. |, 6 3a. -7 b. The quadratic

polynomials are perfect squares. 4. 17 in. by 23 in.

Lesso n Ch eck 1. 4, 7 2. -9, 6 3. §, 3 4. 2.5 ft by 4 ft

6. To solve the equation, you first factor the quadratic

expression, then set each factor equal to 0 , a n d s ol ve.

7. No, if ab = 8 , then there are infinitely many possible
   values of a and b, such as a = 2 and b = 4 or a = - 1
   and b = - 8.
   Ex er cises 9. - | , -7 11. 0, 2.5 13. \ 3 15.


8. -1.5, 12 19. - §, 8 21. -3, 7 23. 1.5, 4 25. ± f


9. 4 ft by^6 ft 29. {-4, -2} 31. {-5, -2} 33. q2 +^
   7q - 18 = 0; -9 , 2 35. x = 2 and x = 1; the
   x-intercepts of the parabola are the same as the zeros of
   the function. 37. 2; ±k 39. 0, 4, 6 41. 0, 3 43. -5 ,
   -1, 1 45. -3 , -2, 3
   Lesson 9-5 pp. 576-581
   Go t I t? 1. 100 2a. -2.21, -6.79 b. No, there are no
   factors of 15 with a sum of 9. 3a. (-2, 6 ) b. (- 6 , 2)


10. 5.77 ft
    Lesso n Ch eck 1. - 1 8 , 10 2. -11, 15 3. -21, 14


11. 
    
    
    
    • 9 , 7.5 5. Answers will vary. Samples are given.
      a. factoring; k2 - 3 k - 304 = (k - 19)(k + 16 )
      b. completing the square 6. Answers will vary. Sample:
      You have to know how to solve using square roots in
      order to solve by completing the square. There are more
      steps involved in completing the square.
      Ex e r c i se s 7. 81 9. 225 11. ^ 13. -16, 9
    
    
    
    


12. -10.24, -5.76 17. -10.12, -1.88 19. (-2, -20)

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