AnswersDHS Algebra 2 VUnit Test

Unit Test — Unit test Answers

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21
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The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?

A
The second parabola opens downward.
B
The second parabola opens upward.
C
The points of intersection are on the x-axis.
D
The points of intersection are of equal distance from the y-axis.
22
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Which equation is the inverse of y = 9x2 – 4?

A
y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction
Option A
B
y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot
Option B
C
y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction
Option C
D
y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds
Option D
23

Which equation is the inverse of ?

Question illustration
A
y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction
Option A
B
y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot
Option B
C
y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot
Option C
D
negative (x minus 4) squared minus two-thirds = negative 6 y + 12
Option D
24

What is one of the solutions to the following system?

Question illustration
A
(–5, 2)
B
(–2, 1)
C
(2, 5)
D
(8, 5)
25

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
26

Solve for in the equation .

Question illustration
A
x = negative 4 plus-or-minus StartRoot 37 EndRoot i
Option A
B
x = –4 ± 5i
C
x = 4 plus-or-minus StartRoot 37 EndRoot i
Option C
D
x = 4 ± 5i
27

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

A
6 units left and 9 units down
B
6 units right and 9 units down
C
6 units left and 9 units up
D
6 units right and 9 units up
28

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

A
The complex numbers have equal imaginary parts.
B
The complex numbers have equal real parts.
C
The complex numbers have opposite imaginary parts.
D
The complex numbers have opposite real parts.
29

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

A
m greater-than StartFraction 25 Over 3 EndFraction
Option A
B
m less-than StartFraction 25 Over 3 EndFraction
Option B
C
m less-than StartFraction 49 Over 12 EndFraction
Option C
D
m greater-than StartFraction 49 Over 12 EndFraction
Option D
30

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
31

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
32

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
33

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

A
The discriminant is less than 0, so there are two real roots.
B
The discriminant is greater than 0, so there are two real roots.
C
The discriminant is less than 0, so there are two complex roots.
D
The discriminant is greater than 0, so there are two complex roots.
34

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true?

A
The circle has a radius greater than 7.
B
The circle has a radius equal to 7.
C
The slope of the line is equal to 7.
D
The slope of the line is not equal to 7.
35

Which values of x and y would make the following expression represent a real number?(4 + 5i)(x + yi)

A
x = 4, y = 5
B
x = –4, y = 0
C
x = 4, y = –5
D
x = 0, y = 5
36

Which system is equivalent to ?

Question illustration
A
StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row 12 x squared + 4 y squared = 22 EndLayout
Option A
B
StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row negative 12 x squared + 4 y squared = 22 EndLayout
Option B
C
StartLayout Enlarged left-brace 1st Row 6 x squared minus 8 y squared = 25 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout
Option C
D
StartLayout Enlarged left-brace 1st Row 6 x squared minus 8 y squared = 50 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout
Option D
37

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.
38

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

A
I
B
II
C
III
D
IV
39

Which equation has a graph that lies entirely above the x-axis?

A
y = –(x + 7)2 + 7
B
y = (x – 7)2 – 7
C
y = (x – 7)2 + 7
D
y = (x – 7)2
40

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

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