AnswersOC27 ALG 2-1200330-S1-Degele-VOL7006PChapter 3 Part 1 Unit TEST: Quadratic Equations and Complex Numbers

Chapter 3 Part 1 Unit TEST: Quadratic Equations and Complex Numbers Answers

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Which statement about the following equation is true?2x2 – 9x + 2 = –1

A
The discriminant is less than 0, so there are two real roots.
B
The discriminant is less than 0, so there are two complex roots.
C
The discriminant is greater than 0, so there are two real roots.
D
The discriminant is greater than 0, so there are two complex roots.
2
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The height of a stuntperson jumping off a building that is 20 m high is modeled by the equation h = 20 – 5t2, where t is the time in seconds. A high-speed camera is ready to film the person between 15 m and 10 m above the ground. For which interval of time should the camera film the person?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
t < 2
3

What is the value of ?

Question illustration
A
–3 + 6i
B
3 + 6i
C
5 + 5i
D
5 – 5i
4

Solve for in the equation .

Question illustration
A
x = 6 plus-or-minus 3 StartRoot 10 EndRoot
Option A
B
x = 6 plus-or-minus 2 StartRoot 7 EndRoot
Option B
C
x = 12 plus-or-minus 3 StartRoot 22 EndRoot
Option C
D
x = 12 plus-or-minus 3 StartRoot 10 EndRoot
Option D
5

Use completing the square to solve for in the equation .

Question illustration
A
x = –1 or 15
B
x = 1 or 7
C
x = 4 plus-or-minus StartRoot 41 EndRoot
Option C
D
x = 4 plus-or-minus StartRoot 73 EndRoot
Option D
6

The graph of a quadratic inequality is shown.

Question illustration
A
y greater-than 3 (x + 15)(x + 3)
Option A
B
y greater-than-or-equal-to (x + 15)(x + 3)
Option B
C
y greater-than 0.25 (x minus 15)(x minus 3)
Option C
D
y greater-than-or-equal-to (x minus 15)(x minus 3)
Option D
7

Which pair of complex numbers has a real-number product?

A
(1 + 2i)(8i)
B
(1 + 2i)(2 – 5i)
C
(1 + 2i)(1 – 2i)
D
(1 + 2i)(4i)
8

In which quadrant is the number 6 – 8i located on the complex plane?

A
I
B
II
C
III
D
IV
9

Using the quadratic formula to solve 4x2 – 3x + 9 = 2x + 1, what are the values of x?

A
StartRoot 1 plus-or-minus StartRoot 159 EndRoot i Over 8 EndFraction
Option A
B
StartRoot 5 plus-or-minus StartRoot 153 EndRoot i Over 8 EndFraction
Option B
C
StartRoot 5 plus-or-minus StartRoot 103 EndRoot i Over 8 EndFraction
Option C
D
StartRoot 1 plus-or-minus StartRoot 153 EndRoot Over 8 EndFraction
Option D
10

What is the distance from the origin to point P graphed on the complex plane below?

Question illustration
A
StartRoot 7 EndRoot
Option A
B
StartRoot 29 EndRoot
Option B
C
7
D
29
11

A quadratic inequality contains the values less than or equal to the quadratic function that has a vertex of (–9, –27) and contains the point on the boundary.

Question illustration
A
y less-than-or-equal-to two-thirds (x minus 9) squared + 27
Option A
B
y less-than-or-equal-to negative two-thirds (x minus 9) squared + 27
Option B
C
y less-than-or-equal-to two-thirds (x + 9) squared minus 27
Option C
D
y less-than-or-equal-to negative two-thirds (x + 9) squared minus 27
Option D
12

Which function is a quadratic function?

A
a(x) = –2x3 + 2x – 6
B
b(x) = 5x3 + 8x2 + 3
C
c(x) = –8x2 + 3x – 5
D
d(x) = 6x4 + 2x – 3
13

A projectile is fired straight up from ground level with an initial velocity of 112 ft/s. Its height, h, above the ground after t seconds is given by h = –16t2 + 112t. What is the interval of time during which the projectile's height exceeds 192 feet?

A
3 < t < 4
B
t < 4
C
t > 4
D
3 > t > 4
14

Which function is a quadratic function?

A
y – 3x2 = 3(x2 + 5) + 1
B
y2 – 7x = 2(x2 + 6) + 7
C
y – 2x2 = 6(x3 + 5) – 4
D
y – 5x = 4(x + 5) + 9
15

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

A
x2 + mx + m = (x – 1)2
B
x2 + mx + m = (x + 1)2
C
x2 + mx + m = (x + 2)2
D
x2 + mx + m = (x + 4)2
16

Which values of p and q would make the value of the following expression equal to 58i? (3 – 7i)(p + qi)i

A
p = 3, q = 7
B
p = –3, q = 7
C
p = 3, q = –7
D
p = –3, q = –7
17

What is the value of the expression i 0 × i 1 × i 2 × i 3 × i 4?

A
1
B
–1
C
i
D
–i
18

What is the additive identity of the complex number 14 + 5i?

A
14 – 5i
B
0
C
1
D
–14 – 5i
19

What is the equation of the axis of symmetry of the graph of y + 3x – 6 = –3(x – 2)2 + 4?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

What is the solution set of the quadratic inequality

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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