AnswersAlgebra 2Quadratics and Complex Numbers

Quadratics and Complex Numbers — Test Answers

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1
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Which quadratic inequality in factored form is represented in the graph?

A
y is greater than 3 open paren x plus 15 close paren open paren x plus 3 close paren
B
y is greater than or equal to open paren x plus 15 close paren times open paren x plus 3 close paren
C
y is greater than or equal to open paren x minus 15 close paren times open paren x minus 3 close paren
D
y is greater than 0 point 2 5 open paren x minus 15 close paren open paren x minus 3 close paren
2
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If the end-of-year analysis indicates that profits did not meet expectations, which inequality in vertex form represents the region containing the results of the year?

A
y is greater than 2 times open paren x minus 25 close paren squared plus 200
B
y is less than negative 2 times open paren x plus 25 close paren squared minus 200
C
y is greater than 2 times open paren x plus 25 close paren squared minus 200
D
y is less than negative 2 times open paren x minus 25 close paren squared plus 200
3

What is the distance from the origin to point cap p graphed on the complex plane?

A
square root of 7
B
square root of 29
C
29
D
7
4

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is 1 fourth the area of the original square. What was the side length of the original square? cap A is equal to s squared

A
12 in.
B
1 in.
C
6 in.
D
2 in.
5

When a baseball is hit by a batter, the height of the ball, h of t , at time t , is determined by the equation h of t is equal to negative 16 t squared plus 64 t plus 4 If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

A
1 is less than t comma t is less than 3
B
t is less than or equal to 1
C
0 is less than t comma t is less than 1
D
1 is less than or equal to t comma t is less than or equal to 3
6

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

A
open paren 1 plus 2 i close paren times open paren 2 minus 5 i close paren
B
open paren 1 plus 2 i close paren times 8 i
C
open paren 1 plus 2 i close paren times open paren 1 minus 2 i close paren
D
open paren 1 plus 2 i close paren times 4 i
7

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? cap v is equal to l w h cap p is equal to 2 times open paren l plus w close paren

A
y is equal to 5 open paren 14 minus x close paren x
B
y is equal to 5 open paren 28 minus x close paren x
C
y is equal to 5 open paren 28 minus 2 x close paren x
D
y is equal to 5 open paren 14 minus 2 x close paren x
8

A company’s profit is modeled by the quadratic function with zeros 6 and 42 The point open paren 15 comma 81 close paren also lies on the boundary line. Any values above the boundary line exceed the expected profits. What is the standard form of the quadratic inequality represented by the description?

A
y is greater than 1 third x squared minus 16 x plus 84
B
y is less than negative 1 third x squared plus 16 x minus 84
C
y is greater than negative 1 third x squared plus 16 x minus 84
D
y is less than 1 third x squared plus 16 x minus 84
9

A quadratic inequality contains the values less than or equal to the quadratic function that has a vertex of open paren negative 9 comma negative 27 close paren and contains the point open paren 1 comma 39 and 2 thirds close paren on the boundary. Which inequality in vertex form represents the description?

A
y is less than or equal to negative 2 thirds times open paren x plus 9 close paren squared minus 27
B
y is less than or equal to 2 thirds times open paren x minus 9 close paren squared plus 27
C
y is less than or equal to 2 thirds times open paren x plus 9 close paren squared minus 27
D
y is less than or equal to negative 2 thirds times open paren x minus 9 close paren squared plus 27
10

What is the value of the expression i to the 0 power times i to the 1th power times i squared times i cubed times i to the 4th power ?

A
i
B
negative 1
C
1
D
negative i
11

Solve for x in the equation x squared minus 8 x plus 41 is equal to 0

A
x is equal to 4 plus or minus 5 i
B
x is equal to 4 plus or minus square root of 37 i
C
x is equal to negative 4 plus or minus 5 i
D
x is equal to negative 4 plus or minus square root of 37 i
12

Using the quadratic formula to solve 4 x squared minus 3 x plus 9 is equal to 2 x plus 1 , what are the values of x ?

A
the fraction with numerator 1 plus or minus square root of 153 and denominator 8
B
the fraction with numerator 5 plus or minus square root of 103 i and denominator 8
C
the fraction with numerator 1 plus or minus square root of 159 i and denominator 8
D
the fraction with numerator 5 plus or minus square root of 153 i and denominator 8
13

Solve for x in the equation x squared minus 12 x plus 36 is equal to 90

A
x is equal to 12 plus or minus 3 square root of 22
B
x is equal to 12 plus or minus 3 square root of 10
C
x is equal to 6 plus or minus 3 square root of 10
D
x is equal to 6 plus or minus 2 square root of 7
14

Which phrase best describes the translation from the graph y is equal to open paren x minus 5 close paren squared plus 7 to the graph of y is equal to open paren x plus 1 close paren squared minus 2 ?

A
6 units right and 9 units down
B
6 units left and 9 units down
C
6 units right and 9 units up
D
6 units left and 9 units up
15

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

A
1
B
negative 14 minus 5 i
C
0
D
14 minus 5 i
16

Which equation is y is equal to 9 x squared plus 9 x minus 1 rewritten in vertex form?

A
y is equal to 9 times open paren x plus 1 half close paren squared minus 13 fourths
B
y is equal to 9 times open paren x plus 1 half close paren squared minus 5 fourths
C
y is equal to 9 times open paren x plus 1 half close paren squared minus 1
D
y is equal to 9 times open paren x plus 1 half close paren squared plus 5 fourths
17

Which statement about the following equation is true? 2 x squared minus 9 x plus 2 is equal to negative 1

A
The discriminant is greater 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 complex roots.
D
The discriminant is less than 0 , so there are two real roots.
18

What is the value of the fraction with numerator 15 i and denominator 2 plus i ?

A
5 plus 5 i
B
negative 3 plus 6 i
C
5 minus 5 i
D
3 plus 6 i
19

What is the solution set of the quadratic inequality x squared minus 5 is less than or equal to 0 ?

A
start set x such that negative square root of 5 is less than or equal to x comma x is less than or equal to 5 end set
B
start set x such that negative square root of 5 is less than or equal to x comma x is less than or equal to square root of 5 end set
C
start set x such that negative 5 is less than or equal to x comma x is less than or equal to 5 end set
D
start set x such that negative 5 is less than or equal to x comma x is less than or equal to square root of 5 end set
20

Which statement about the following equation is true? 3 x squared minus 8 x plus 5 is equal to 5 x squared

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 complex roots.
D
The discriminant is greater than 0 , so there are two real roots.

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