AnswersMathematics IIQuadratic Functions and Complex Numbers

Quadratic Functions and Complex Numbers — Test Answers

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Which is a potential rational root of f of x at point cap p ?

A
The root at point cap p may be 1 fifth .
B
The root at point cap p may be 1 third .
C
The root at point cap p may be 5 thirds .
D
The root at point cap p may be 3 fifths .
2
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What is the distance from the origin to point cap p graphed on the complex plane?

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

Which equation represents x , the side length of the greater square?

A
x squared plus 2 x squared is equal to 10
B
x squared plus open paren x minus 2 close paren squared is equal to 100
C
x squared plus 2 x squared is equal to 100
D
x squared plus open paren x minus 2 close paren squared is equal to 10
5

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 plus 5 fourths
D
y is equal to 9 times open paren x plus 1 half close paren squared minus 5 fourths
6

According to the Rational Root Theorem, which is a factor of the polynomial f of x is equal to 3 x cubed minus 5 x squared minus 12 x plus 20 ?

A
2 x minus 1
B
2 x plus 1
C
3 x plus 5
D
3 x minus 5
7

Which equation demonstrates the multiplicative identity property?

A
open paren negative 3 plus 5 i close paren plus 0 is equal to negative 3 plus 5 i
B
open paren negative 3 plus 5 i close paren times 1 is equal to negative 3 plus 5 i
C
open paren negative 3 plus 5 i close paren times open paren negative 3 plus 5 i close paren is equal to negative 16 minus 30 i
D
open paren negative 3 plus 5 i close paren times open paren 3 minus 5 i close paren is equal to 16 plus 30 i
8

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 12 x plus 2
B
y is equal to 4 x squared plus 24 x plus 38
C
y is equal to 4 x squared minus 24 x plus 38
D
y is equal to 4 x squared plus 16 x plus 13
9

Which represents the solution(s) of the graphed system of equations, y is equal to x squared minus 2 x and y is equal to negative 2 x minus 1 ? Expand Image

A
1 comma negative 1
B
0 comma 0 and 0 comma negative 1
C
0 comma 0 and 2 comma 0
D
no solutions
10

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 5 plus or minus square root of 153 i 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 153 and denominator 8
D
the fraction with numerator 1 plus or minus square root of 159 i and denominator 8
11

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 open paren 1 minus i close paren plus open paren 21 plus 5 i close paren
B
negative 1 plus open paren i plus 21 close paren plus 5 i
C
open paren negative 1 plus 21 close paren plus open paren i plus 5 i close paren
D
open paren negative 1 plus i close paren plus open paren 21 plus 5 i close paren plus 0
12

Which of the following describes the roots of the polynomial function f of x is equal to open paren x plus 2 close paren squared times open paren x minus 4 close paren times open paren x plus 1 close paren cubed ?

A
2 with multiplicity 2 comma negative 4 with multiplicity 1 , and 1 with multiplicity 3
B
negative 2 with multiplicity 2 comma 4 with multiplicity 1 , and negative 1 with multiplicity 3
C
2 with multiplicity 3 comma negative 4 with multiplicity 2 , and 1 with multiplicity 4
D
negative 2 with multiplicity 3 comma 4 with multiplicity 2 comma and negative 1 with multiplicity 4
13

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 less than 0 , so there are two complex roots.
B
The discriminant is greater 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 less than 0 , so there are two real roots.
14

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
negative i
B
1
C
i
D
negative 1
15

According to the Rational Root Theorem, what are all the potential rational roots of f of x is equal to 5 x cubed minus 7 x plus 11 ?

A
plus or minus 1 over 11 , plus or minus 5 over 11 , plus or minus 1 , plus or minus 5
B
plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
C
plus or minus 1 fifth , plus or minus 1 , plus or minus 11 fifths , plus or minus 11
D
0 , plus or minus 1 over 11 , plus or minus 1 fifth , plus or minus 5 over 11 , plus or minus 1 , plus or minus 11 fifths , plus or minus 5 , plus or minus 11
16

The sum of a number and its square is 42 Which equation can be used to find the two numbers for which this is true?

A
x squared plus 2 x is equal to 42
B
x squared plus x is equal to 42
C
x squared plus x plus 42 is equal to 0
D
x squared plus 2 x plus 42 is equal to 0
17

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 2 square root of 7
B
x is equal to 12 plus or minus 3 square root of 10
C
x is equal to 12 plus or minus 3 square root of 22
D
x is equal to 6 plus or minus 3 square root of 10
18

A rectangle’s length is three times its width, w Its area is 243 square units. Which equation can be used to find the width of the rectangle?

A
4 w squared is equal to 243
B
3 w squared is equal to 243
C
w squared is equal to 3 times 243
D
3 w squared is equal to 3 times 243
19

Which statement describes the graph of this polynomial function? f of x is equal to x to the 5th power minus 6 x to the 4th power plus 9 x cubed

A
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to negative 3 .
B
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to negative 3 .
C
The graph crosses the x -axis at x is equal to 0 and touches the x -axis at x is equal to 3 .
D
The graph touches the x -axis at x is equal to 0 and crosses the x -axis at x is equal to 3 .
20

A rectangle has an area of 40 square units. The length is 6 units greater than the width. What are the dimensions of the rectangle?

A
13 by 7
B
8 by 5
C
11 by 9
D
10 by 4
21

Which represents the solution(s) of the graphed system of equations, y is equal to negative x squared plus x plus 2 and y is equal to negative x plus 3 ? Expand Image

A
1 comma 2
B
1 comma 2 and 0 comma 3
C
2 comma 1
D
negative 1 comma 0 and 2 comma 0

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