AnswersAlgebra IIQuadratics and Complex Numbers

Quadratics and Complex Numbers — Test Answers

24 verified answers2 views
3

Which equation is the inverse of y is equal to 9 x squared minus 4 ?

A
y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 9
B
y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 3
C
y is equal to the fraction with numerator plus or minus square root of x and denominator 3 plus 2 thirds
D
y is equal to plus or minus square root of x over 9 plus 4 end root
4

Which equation represents a graph with a vertex at open paren negative 3 comma 2 close paren ?

A
y is equal to 4 x squared plus 24 x plus 38
B
y is equal to 4 x squared plus 12 x plus 2
C
y is equal to 4 x squared plus 16 x plus 13
D
y is equal to 4 x squared minus 24 x plus 38
6

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 greater than 0 , so there are two complex roots.
B
The discriminant is less than 0 , so there are two real roots.
C
The discriminant is greater than 0 , so there are two real roots.
D
The discriminant is less than 0 , so there are two complex roots.
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 28 minus 2 x close paren x
B
y is equal to 5 open paren 14 minus x close paren x
C
y is equal to 5 open paren 14 minus 2 x close paren x
D
y is equal to 5 open paren 28 minus x close paren x
8

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 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 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 square root of 5 end set
D
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
9

Use the zero product property to find the solutions to the equation x squared plus x minus 30 is equal to 12

A
x is equal to negative 6 or x is equal to 7
B
x is equal to 6 or x is equal to 7
C
x is equal to negative 7 or x is equal to negative 6
D
x is equal to negative 7 or x is equal to 6
11

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 159 i and denominator 8
B
the fraction with numerator 1 plus or minus square root of 153 and denominator 8
C
the fraction with numerator 5 plus or minus square root of 153 i and denominator 8
D
the fraction with numerator 5 plus or minus square root of 103 i and denominator 8
12

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

Which equation is the inverse of open paren x minus 4 close paren squared minus 2 thirds is equal to 6 y minus 12 ?

A
negative open paren x minus 4 close paren squared minus 2 thirds is equal to negative 6 y plus 12
B
y is equal to 4 plus or minus square root of 6 x minus 34 thirds end root
C
y is equal to 1 sixth x squared minus 4 thirds x plus 43 ninths
D
y is equal to negative 4 plus or minus square root of 6 x minus 34 thirds end root
15

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 complex roots.
B
The discriminant is less 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 real roots.
17

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression open paren negative 1 plus i close paren plus open paren 21 plus 5 i close paren ?

A
negative 1 plus open paren i plus 21 close paren plus 5 i
B
open paren negative 1 plus 21 close paren plus open paren i plus 5 i close paren
C
open paren negative 1 plus i close paren plus open paren 21 plus 5 i close paren plus 0
D
negative open paren 1 minus i close paren plus open paren 21 plus 5 i close paren
18

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

A
x is equal to 6 plus or minus 3 square root of 10
B
x is equal to 12 plus or minus 3 square root of 22
C
x is equal to 6 plus or minus 2 square root of 7
D
x is equal to 12 plus or minus 3 square root of 10
20

Use the zero product property to find the solutions to the equation 6 x squared minus 5 x is equal to 56

A
x is equal to negative 8 thirds or x is equal to 7 halves
B
x is equal to negative 1 half or x is equal to 56 thirds
C
x is equal to negative 8 or x is equal to 7 sixths
D
x is equal to negative 3 sevenths or x is equal to 2 thirds

Did you find these answers helpful?