AnswersAlgebra IIQuadratics and Complex Numbers

Quadratics and Complex Numbers — Test Answers

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Which function is a quadratic function?

A
y squared minus 7 x is equal to 2 times open paren x squared plus 6 close paren plus 7
B
y minus 3 x squared is equal to 3 times open paren x squared plus 5 close paren plus 1
C
y minus 5 x is equal to 4 times open paren x plus 5 close paren plus 9
D
y minus 2 x squared is equal to 6 times open paren x cubed plus 5 close paren minus 4
3

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 plus 5 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 minus 1
5

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

A
y is equal to open paren x minus 7 close paren squared plus 7
B
y is equal to negative open paren x plus 7 close paren squared plus 7
C
y is equal to open paren x minus 7 close paren squared
D
y is equal to open paren x minus 7 close paren squared minus 7
6

Which values of x and y would make the following expression represent a real number? open paren 4 plus 5 i close paren times open paren x plus y i close paren

A
x is equal to 4 , y is equal to negative 5
B
x is equal to negative 4 , y is equal to 0
C
x is equal to 4 , y is equal to 5
D
x is equal to 0 , y is equal to 5
7

For what values of m does the graph of y is equal to 3 x squared plus 7 x plus m have two x -intercepts?

A
m is less than 49 over 12
B
m is greater than 25 thirds
C
m is less than 25 thirds
D
m is greater than 49 over 12
8

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.
9

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 8 or x is equal to 7 sixths
C
x is equal to negative 1 half or x is equal to 56 thirds
D
x is equal to negative 3 sevenths or x is equal to 2 thirds
10

If x is equal to negative 3 is the only x -intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

A
The discriminant is 0 .
B
The discriminant is negative .
C
The discriminant is negative 3 .
D
The discriminant is positive.
12

Which function is a quadratic function?

A
b times x is equal to 5 x cubed plus 8 x squared plus 3
B
c times x is equal to negative 8 x squared plus 3 x minus 5
C
d times x is equal to 6 x to the 4th power plus 2 x minus 3
D
A times x is equal to negative 2 x cubed plus 2 x minus 6
13

Which equation demonstrates the multiplicative identity property?

A
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
B
open paren negative 3 plus 5 i close paren plus 0 is equal to negative 3 plus 5 i
C
open paren negative 3 plus 5 i close paren times 1 is equal to negative 3 plus 5 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
14

What is the value of open paren negative 7 plus 3 i close paren minus open paren 2 minus 6 i close paren ?

A
negative 9 plus 9 i
B
negative 9 minus 3 i
C
negative 5 plus 9 i
D
negative 5 minus 3 i
15

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
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 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
18

The square of a number is 12 less than 7 times the number. What is the number?

A
negative 3 or 4
B
3 or 4
C
negative 4 or 3
D
negative 4 or negative 3
19

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34 i 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 real parts.
D
The complex numbers have opposite imaginary parts.
20

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 6
D
x is equal to negative 7 or x is equal to negative 6

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