3) (9 5i B) 85 5i C) 5 85i D) 40i2 5i 45 4) ( 6 39 39i B ......Page 3) (9 + 8i)(5 - 5i) A) 85 - 5i...

) (9 + 8i)(5 - 5i)

A) 85 - 5i B) 85 + 5i C) 5 + 85i D) -40i2 - 5i + 45

4) (-6 + 9i)(5 + i)

A) -39 + 39i B) -21 + 39i C) -39 - 51i D) -21 - 51i

5) (8 - 6i)(-5 - 3i)

A) -58 + 6i B) -58 - 54i C) -22 + 6i D) -22 - 54i

6) (9 + 3i)(9 - 3i)

A) 90 B) 81 - 9i2 C) 72 D) 81 - 9i

Full file at https://testbank123.eu/Test-Bank-for-Precalculus-Essentials-5th-Edition-Blitzer


https://testbank123.eu/Test-Bank-for-Precalculus-Essentials-5th-Edition-Blitzer

) (-4 + i)(-4 - i) A) 17 B) -4 C) 16 D) -15

8) (4 + 9i)2

A) -65 + 72i

B) 97 + 72i

C) -65

D) 16 + 72i + 81i2

Perform the indicated operations and write the result in standard form. 9) (7 + 8i)(3 - i) - (1 - i)(1 + i)

A) 27 + 17i B) 31 + 17i C) 29 + 17i D) 27 + 31i

10) (2 + i)2 - (6 - i)2

A) -32 + 16i B) 32 + 16i C) -48 D) -32 - 16i

Complex numbers are used in electronics to describe the current in an electric circuit. Ohm's law relates the current

in a circuit, I, in amperes, the voltage of the circuit, E, in volts, and the resistance of the circuit, R, in ohms, by the

formula E = IR. Solve the problem using this formula.

11) Find E, the voltage of a circuit, if I = (8 + 9i) amperes and R = (4 + 7i) ohms.

A) (-31 + 92i) volts B) (-31 - 92i) volts C) (92 - 31i) volts D) (92 + 31i) volts

12) Find E, the voltage of a circuit, if I = (18 + i) amperes and R = (2 + 3i) ohms.

A) (33 + 56i) volts B) (33 - 56i) volts C) (-18 + 56i) volts D) (-18 - 56i) volts

3 Divide Complex Numbers

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Divide and express the result in standard form.

1) 7 8 - i

A) 56

+ 7

i B) 56

- 7

i C) 8

+ 1

i D) 8

- 1

i65 65 65 65 9 9 9 9

2) 8 2 + i

A) 16

- 8

i B) 16

+ 8

i C) 16

+ 8

i D) 16

- 8

i5 5 5 5 3 3 3 3

3) 10i 3 + i

A) 1 + 3i B) -1 + 3i C) 1 + 10i D) 1 - 3i

4) 4i 3 + i

2 6 2 6 1 3 2 6A) 5

+ 5

i B) - 5

+ 5

i C) 2

+ 2

i D) 5

- 5

i

5) 2i 1 + 7i

7

1

1

7

7

1

1

7 A)

25 +

25 i B)

25 +

25 i C) -

24 +

24 i D) -

24 -

24 i





) 4 + 5i 5 - 4i

A) i

B) -i

C) 1

D) -1

7) 5 - 4i 8 + 6i

A) 4

- 31

i 25 50

B) 2

- 31

i 7 28

C) 32

+ 1

i 25 25

D) 16

- 31

i 7 28

8) 3 + 4i 9 - 3i

A) 1

+ 1

i 6 2

B) 1

+ 1

i 72 24

C) 13

- 9

i 2 2

D) 13

+ 1

i 24 24

9) 2 + 3i 5 + 2i

A) 16

+ 11

i B) 16

+ 11

i C) 4

- 19

i D) 4

+ 11

i 29 29 21 21 29 29 21 21

10) 5 + 8i 4 + 2i

A) 9

+ 11

i B) 3

+ 11

i C) 2

- 21

i D) 1

+ 11

i 5 10 2 12 5 5 3 12

11) 4 - 3i 5 - 3i

A) 29

- 3

i B) 29

- 3

i C) 11

+ 27

i D) 11

- 3

i 34 34 16 16 34 34 16 16

4 Perform Operations with Square Roots of Negative Numbers


Perform the indicated operations and write the result in standard form.

1) -16 + -81 A) 13i

2) -3 - -121

B) -13i C) 36i D) -13

A) i( 3 - 11) B) 3i - 11 C) 3i - 11i D) i( 3 + 11)

3) 3 -64 + 4 -49

A) 52i

B) -52

C) 52

D) -52i

4) 2 -32 + 5 -50

A) 33i 2 B) -33 2 C) 33 2 D) -33i 2

5) (-8 - -49)2

A) 15 + 112i B) 113 + 112i C) 64 + 49i D) 64 - 49i





) (-6 + -100)2

A) -64 - 120i B) 136 + 120i C) 36 + 100i D) 36 - 100i

7) ( 6 - - 64)( 6 + - 64)

A) 70 B) -58 C) 6 - 64i D) 6 - 8i

8) (3 + -3) (3 + -2)

A) (9 - 6 )+ (3 2 + 3 3)i B) (9 + 6 )- 15i

C) 3 - 6 6i D) 15 + 36i

9) -2 + -12

2

A) -1 + i 3 B) -1 - i 3 C) 1 + i 3 D) -1 + i 2

10) -42 - -252

6

A) -7 - i 7 B) -7 + i 7 C) 7 + i 7 D) -7 - i 6

11) -16(5 - -9)

A) 12 + 20i

B) 20i - 12

C) 20i - 12i2

D) 20i + 12i2

12) ( -9)( -64)

A) -24

B) 24i2

C) 24

D) -24i

5 Solve Quadratic Equations with Complex Imaginary Solutions


Solve the quadratic equation using the quadratic formula. Express the solution in standard form.

1) x2 + x + 2 = 0

A) - 1

± i 7 B)

1 ± i

7 C) 1

± 7 D) -

1 ±

7

2 2 2 2 2 2 2 2

2) x2 - 12x + 40 = 0

A) {6 ± 2i} B) {6 ± 4i} C) {6 + 2i} D) {4, 8}

3) 8x2 + 3x + 3 = 0

A) - 3

± i 87

B) - 3

± 87

C) 3

± i 87

D) 3

± 87

16 16 16 16 16 16 16 16

4) 16x2 - 5x + 1 = 0

A) 5

± i 39

B) - 5

± i 39

C) - 5

± 39

D) 5

± 39

32 32 32 32 32 32 32 32

5) 5x2 = -9x - 7

A) - 9

± i 59

B) - 9

± 59

C) 9

± i 59

D) 9

± 59

10 10 10 10 10 10 10 10





2 Quadratic Functions

1 Recognize Characteristics of Parabolas


The graph of a quadratic function is given. Determine the function's equation.

1)

10

8

6

4

2

-10 -8 -6 -4 -2

-2

-4

-6

-8

-10

y

2 4 6 8 10 x

A) f(x) = (x + 3)2 + 3 B) g(x) = (x + 3)2 - 3 C) h(x) = (x - 3)2 + 3 D) j(x) = (x - 3)2 - 3

2)

10

8

6

4

2

-10 -8 -6 -4 -2

-2

-4

-6

-8

-10

y

2 4 6 8 10 x

A) g(x) = (x + 3)2 - 3 B) f(x) = (x + 3)2 + 3 C) h(x) = (x - 3)2 + 3 D) j(x) = (x - 3)2 - 3

3)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) h(x) = (x - 2)2 + 2 B) g(x) = (x + 2)2 - 2 C) f(x) = (x + 2)2 + 2 D) j(x) = (x - 2)2 - 2





)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) j(x) = (x - 2)2 - 2 B) g(x) = (x + 2)2 - 2 C) h(x) = (x - 2)2 + 2 D) f(x) = (x + 2)2 + 2

5)

10

8

6

4

2

-10 -8 -6 -4 -2

-2

-4

-6

-8

-10

y

2 4 6 8 10 x

A) f(x) = x2 - 4x + 4 B) g(x) = x2 + 4x + 4 C) h(x) = x2 - 2 D) j(x) = x2 + 2

6)

10

8

6

4

2

-10 -8 -6 -4 -2

-2

-4

-6

-8

-10

y

2 4 6 8 10 x

A) g(x) = x2 + 2x + 1 B) f(x) = x2 - 2x + 1 C) h(x) = x2 - 1 D) j(x) = x2 + 1





)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) h(x) = x2 - 1 B) g(x) = x2 + 2x + 1 C) f(x) = x2 - 2x + 1 D) j(x) = x2 + 1

8)

10

8

6

4

2

-10 -8 -6 -4 -2

-2

-4

-6

-8

-10

y

2 4 6 8 10 x

A) j(x) = x2 + 3 B) g(x) = x2 + 6x + 9 C) h(x) = x2 - 3 D) f(x) = x2 - 6x + 9

9)

10

8

6

4

2

-10 -8 -6 -4 -2

-2

-4

-6

-8

-10

y

2 4 6 8 10 x

A) j(x) = -x2 + 2 B) g(x) = -x2 + 4x + 4 C) h(x) = -x2 - 2 D) f(x) = -x2 - 4x - 4





Page

A) (-1, 1)

12) f(x) = x2 + 8

B) (-1, -1) C) (0, 1) D) (1, 0)

A) (0, 8) B) (-8, 0) C) (0, -8) D) (8, 0)

13) f(x) = (x + 5)2 + 9

A) (-5, 9) B) (-9, 5) C) (9, -25) D) (9, -5)

14) f(x) = 9 - (x + 5)2

A) (-5, 9) B) (5, 9) C) (9, 5) D) (9, -5)

15) f(x) = (x + 3)2 - 2

A) (-3, -2) B) (3, 2) C) (3, -2) D) (-3, 2)

16) y + 4 = (x + 2)2

A) (- 2, - 4) B) (2, - 4) C) (4, - 2) D) (4, 2)

17) f(x) = 11(x - 5)2 + 9

A) (5, 9) B) (11, 5) C) (-5, 9) D) (9, -5)

18) f(x) = -7(x - 2)2 - 8

A) (2, -8) B) (-8, 2) C) (-2, -8) D) (-7, -2)

19) f(x) = x2 - 8

A) (0, -8) B) (1, 0) C) (0, 8) D) (8, 0)

20) f(x) = x2 + 12x - 1

A) (-6, -37) B) (6, 107) C) (12, 287) D) (-6, -109)

21) f(x) = -x2 + 14x + 8

A) (7, 57)

B) (-7, -139)

C) (14, 8)

D) (-7, -41)

10)

y

10

8

6

4

2

-10 -8 -6 -4 -2 2 4 6 8 10 x -2

-4

-6

-8

-10

A) h(x) = -x2 - 1 B) g(x) = -x2 + 2x + 1 C) j(x) = -x2 + 1 D) f(x) = -x2 - 2x - 1

Find the coordinates of the vertex for the parabola defined by the given quadratic function.

11) f(x) = (x + 1)2 + 1





Page

A) [6, ∞)

35) f(x) = (x + 4)2 + 8

B) (-∞, 6] C) [-6, ∞) D) [0, ∞)

A) [8, ∞) B) [-8, ∞) C) [4, ∞) D) [-4, ∞)

36) f(x) = 4 - (x + 2)2

A) (-∞, 4]

B) [4, ∞)

C) (-∞, 2]

D) [-2, ∞)

37) f(x) = (x + 8)2 - 3

A) [-3, ∞)

B) (-∞, -8]

C) (-∞, -3]

D) [-8, ∞)

22) f(x) = 8 - x2 + 2x

A) (1, 9) B) (- 1, 9) C) (1, - 9) D) (- 1, - 9)

23) f(x) = -6x2 - 12x + 4

A) (-1, 10) B) (1, -14) C) (-2, -8) D) (2, -44)

Find the axis of symmetry of the parabola defined by the given quadratic function.

24) f(x) = x2 + 7

A) x = 0

25) f(x) = (x + 3)2 + 7

B) x = 7 C) x = -7 D) y = 7

A) x = -3 B) x = 3 C) y = 7 D) y = -7

26) f(x) = 6 - (x + 3)2

A) x = -3 B) x = 3 C) x = 6 D) x = -6

27) f(x) = (x + 1)2 - 9

A) x = -1 B) x = 1 C) x = -9 D) x = 9

28) y + 9 = (x - 3)2

A) x = 3

B) x = - 3

C) y = 9

D) y = -9

29) f(x) = 11(x - 3)2 + 7

A) x = 3 B) x = 11 C) x = -3 D) x = 7

30) f(x) = -7(x - 4)2 - 6

A) x = 4 B) x = -6 C) x = -4 D) x = -7

31) f(x) = x2 + 12x - 5

A) x = -6 B) x = 6 C) x = 12 D) x = -41

32) f(x) = -x2 + 2x - 3

A) x = 1 B) x = -1 C) x = 2 D) x = -2

33) f(x) = 2x2 + 4x - 7

A) x = -1 B) x = 1 C) x = -2 D) x = -9

Find the range of the quadratic function.

34) f(x) = x2 + 6





) y + 4 = (x - 2)2

A) [- 4, ∞)

39) f(x) = 11(x - 4)2 + 5

B) (-∞, - 2] C) [4, ∞) D) (-∞, 4]

A) [5, ∞) B) [4, ∞) C) (-∞, 5] D) [-5, ∞)

40) f(x) = -7(x - 5)2 - 7

A) (-∞, -7] B) (-∞, 5] C) [-7, ∞) D) [-5, ∞)

41) f(x) = x2 - 8x - 8

A) [-24, ∞) B) [-4, ∞) C) (-∞, -24] D) (-∞, -56]

42) f(x) = -x2 + 10x + 3

A) (-∞, 28] B) [28, ∞) C) [5, ∞) D) (-∞, 5]

43) f(x) = 2x2 + 3x - 9

A) [- 81

, ∞) B) (-∞, - 81

] C) [- 3

, ∞) D) (-∞, - 3

] 8 8 4 4

44) f(x) = -3x2 - 6x

A) (-∞, 3] B) (-∞, - 3] C) (-∞, - 1] D) (-∞, 1]

Find the x-intercepts (if any) for the graph of the quadratic function.

45) f(x) = x2 - 4

A) (-2, 0) and (2, 0) B) (-4, 0) C) (2, 0) D) No x-intercepts

46) f(x) = (x - 1)2 - 1

A) (0, 0) and (2, 0) B) (0, 0) and (-2, 0) C) (0, 0) and (-1, 0) D) (-2, 0) and (2, 0)

47) y + 4 = (x - 2)2

A) (0, 0) and (4, 0) B) (0, 0) and (-4, 0) C) (-4, 0) and (4, 0) D) (0, 0)

48) f(x) = 4 + 5x + x2

A) (-1, 0) and (-4, 0) B) (1, 0) and (4, 0) C) (1, 0) and (-4, 0) D) (-1, 0) and (4, 0)

49) f(x) = x2 + 18x + 67 Give your answers in exact form.

A) (-9 ± 14, 0) B) (9 + 14, 0) C) (9 ± 67, 0) D) (-18 ± 67, 0)

50) f(x) = -x2 + 11x - 30

A) (5, 0) and (6, 0) B) (-5, 0) and (-6, 0) C) (5, 0) and (-6, 0) D) No x-intercepts

51) f(x) = 2x2 - 9x + 10

A) (2, 0) and (2.5, 0) B) (2, 0) and (-2.5, 0) C) (5, 0) and (1, 0) D) (5, 0) and (-1, 0)

52) f(x) = 2x2 + 26x + 72

A) (-4, 0) and (-9, 0) B) (4, 0) and (9, 0) C) (-4, 0) and (9, 0) D) (4, 0) and (-9, 0)





) 3x2 + 6x + 2 = 0

Give your answers in exact form.

A) -3 ± 3

, 0 B) -3 ± 3

, 0 C) -6 ± 3

, 0 D) -3 ± 15

, 0 3 6 3 3

Find the y-intercept for the graph of the quadratic function.

54) f(x) = -x2 - 2x + 8

A) (0, 8) B) (8, 0) C) (0, -4) D) (0, -8)

55) y + 9 = (x - 3)2

A) (0, 0) B) (0, -6) C) (0, 6) D) (9, 0)

56) f(x) = 4 + 5x + x2

A) (0, 4) B) (0, 1) C) (0, -4) D) (0, 5)

57) f(x) = x2 + 5x - 6

A) (0, -6) B) (0, 3) C) (0, 6) D) (0, 5)

58) f(x) = (x + 3)2 - 9

A) (0, 0) B) (0, 6) C) (0, 9) D) (0, -9)

59) f(x) = 4x2 - 3x - 7

A) (0, -7) B) (0, 7) C) 0, 7 4

D) 0, - 7 4

Find the domain and range of the quadratic function whose graph is described.

60) The vertex is (1, -14) and the graph opens up.

A) Domain: (-∞, ∞)

Range: [-14, ∞)

B) Domain: [1, ∞)

Range: [-14, ∞)

C) Domain: (-∞, ∞)

Range: (-∞, -14]

D) Domain: (-∞, ∞)

Range: [1, ∞)

61) The vertex is (-1, -10) and the graph opens down.

A) Domain: (-∞, ∞)

Range: (-∞, -10]

B) Domain: (-∞, -1]

Range: (-∞, -10]

C) Domain: (-∞, ∞)

Range: [-10, ∞)

D) Domain: (-∞, ∞)

Range: (-∞, -1]

62) The minimum is 0 at x = -1.

A) Domain: (-∞, ∞) Range: [0, ∞)

B) Domain: [-1, ∞) Range: [0, ∞)

C) Domain: (-∞, ∞) Range: (-∞, 0]

D) Domain: (-∞, ∞) Range: [-1, ∞)

63) The maximum is -8 at x = 1

A) Domain: (-∞, ∞) B) Domain: (-∞, 1] C) Domain: (-∞, ∞) D) Domain: (-∞, ∞)

Range: (-∞, -8] Range: (-∞, -8] Range: [-8, ∞) Range: (-∞, 1]

Solve the problem.

64) Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 11x2, but

which has its vertex at (3, 4).

A) f(x) = 11(x - 3)2 + 4 B) f(x) = 11(x + 3)2 + 4

C) f(x) = (11x + 3)2 + 4 D) f(x) = 11(x + 4)2 + 3





) Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 5x2, but

which has a minimum of 7 at x = 3.

A) f(x) = 5(x - 3)2 + 7 B) f(x) = 5(x + 3)2 + 7

C) f(x) = -5(x - 3)2 + 7 D) f(x) = 5(x + 7)2 - 3

66) Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = -7x2, but

which has a maximum of 7 at x = 5.

A) f(x) = -7(x - 5)2 + 7 B) f(x) = -7(x + 5)2 + 7

C) f(x) = 7(x - 5)2 + 7 D) f(x) = -7(x - 5)2 - 7





Graph Parabolas


Use the vertex and intercepts to sketch the graph of the quadratic function.

1) y - 4 = (x + 5)2

y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





) f(x) = -3(x - 6)2 - 3 y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





) f(x) = (x - 5)2 - 6

y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





) f(x) = 1 - (x + 1)2

y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





) f(x) = x2 + 6x + 5

y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





) f(x) = -x2 - 4x + 5

y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





) f(x) = x2 - 8x + 7

y

10

5

-10 -5 5 10 x

-5

-10

A) B)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10

C) D)

y y

10 10

5 5

-10 -5 5 10 x -10 -5 5 10 x

-5

-10

-5

-10





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