AnswersMathematics IIQuadratic Functions and Complex Numbers

Practice Test Answers

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1
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Which equation can be used to find the dimensions of the patio?

A
x squared plus open paren x plus 5 close paren squared is equal to 29
B
x squared plus open paren x plus 5 close paren squared is equal to 841
C
0 point 5 x open paren x plus 5 close paren is equal to 29
D
0 point 5 x open paren x plus 5 close paren is equal to 841
2
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What are the values of x in the equation x squared minus 6 x plus 9 is equal to 25 ?

A
x is equal to 2 or x is equal to negative 8
B
x is equal to negative 2 or x is equal to 8
C
x is equal to negative 1 or x is equal to negative 11
D
x is equal to 1 or x is equal to 11
3

Dimitri is solving the equation x squared minus 10 x is equal to 21 Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

A
100
B
4
C
0
D
25
4

Which statement describes the graph of this polynomial function? f of x is equal to x to the 4th power plus x cubed minus 2 x squared

A
The graph crosses the x -axis at x is equal to negative 2 and x is equal to 1 and touches the x -axis at x is equal to 0 .
B
The graph touches the x -axis at x is equal to negative 2 and x is equal to 1 and crosses the x -axis at x is equal to 0 .
C
The graph crosses the x -axis at x is equal to 2 and x is equal to negative 1 and touches the x -axis at x is equal to 0 .
D
The graph touches the x -axis at x is equal to 2 and x is equal to negative 1 and crosses the x -axis at x is equal to 0 .
5

According to the Rational Root Theorem, the following are potential roots of f of x is equal to 6 x to the 4th power plus 5 x cubed minus 33 x squared minus 12 x plus 20 negative 5 halves , negative 2 , 1 , 10 thirds Which is an actual root of f of x ?

A
negative 5 halves
B
negative 2
C
10 thirds
D
1
6

Which graph shows a system of equations with a solution at 2 comma negative 1 ?

A
Image with description On a coordinate plane, the scale on the x and the y axes ranges from negative 5 to 5 in increments of 1. A parabola opens down and has the vertex at 0 comma 1. A straight line has a positive slope, passing through the points 0 comma negative 3 and 3 comma 0.
B
Image with description On a coordinate plane, the scale on the x and the y axes ranges from negative 5 to 5 in increments of 1. A parabola opens up and has a vertex at 0 coma negative 3. A straight line has a negative slope, passes through the points negative 3 comma 0 and 0 comma negative 3
C
Image with description On a coordinate plane, the scale on the x and the y axes ranges from negative 5 to 5 in increments of 1. A parabola opens down and has a vertex at 0 comma 3. A straight line has a positive slope, passes through the points 1 comma 0 and 0 comma negative 1.
D
Image with description On a coordinate plane, the scale on the x and the y axes ranges from negative 5 to 5 in increments of 1. A parabola opens up and has a vertex at 0 coma negative 2. A straight line has a positive slope, passes through the points 1 comma 0 and 0 comma negative 1.
7

Clara writes the equation open paren x minus 13 close paren times open paren x plus 8 close paren is equal to 196 to solve for the missing side length of a rectangle represented by the factor x plus 8 What is the missing side length represented by x plus 8 units of the rectangle?

A
20
B
28
C
7
D
15
8

Two numbers are 10 units away in different directions from their midpoint, m , on a number line. The product of the numbers is negative 99 Which equation can be used to find m , the midpoint of the two numbers?

A
m squared minus 25 is equal to negative 99
B
m squared minus 100 is equal to negative 99
C
open paren m minus 10 close paren times open paren m plus 10 close paren is equal to 99
D
open paren m minus 5 close paren times open paren m plus 5 close paren is equal to 99
9

The first two steps in determining the solution set of the system of equations, y is equal to negative x squared plus 4 x plus 12 and y is equal to negative 3 x plus 24 , algebraically are shown in the table. Step Equation Step 1 negative x squared plus 4 x plus 12 is equal to negative 3 x plus 24 Step 2 x squared minus 7 x plus 12 is equal to 0 Which represents the solution(s) of this system of equations?

A
3 comma 15
B
negative 3 comma 33 and negative 4 comma 36
C
negative 4 comma 36
D
3 comma 15 and 4 comma 12
10

Using the quadratic formula to solve 11 x squared minus 4 x is equal to 1 , what are the values of x ?

A
2 over 11 plus or minus the fraction with numerator square root of 7 and denominator 11
B
2 over 11 plus or minus the fraction with numerator square root of 15 and denominator 11
C
2 over 11 plus or minus the fraction with numerator square root of 7 i and denominator 11
D
2 over 11 plus or minus the fraction with numerator 2 square root of 15 and denominator 11
11

Which equation is y is equal to 3 times open paren x minus 2 close paren squared minus open paren x minus 5 close paren squared rewritten in vertex form?

A
y is equal to 2 times open paren x minus 1 half close paren squared minus 27 halves
B
y is equal to 3 times open paren x minus 7 halves close paren squared minus 27 fourths
C
y is equal to 2 times open paren x minus 1 close paren squared minus 11
D
y is equal to 2 times open paren x minus 1 half close paren squared minus 53 fourths
12

If 5 plus 6 i is a root of the polynomial function f of x , which of the following must also be a root of f of x ?

A
6 plus 5 i
B
5 minus 6 i
C
negative 5 minus 6 i
D
6 minus 5 i
13

Which expression is equivalent to open paren 4 plus 6 i close paren squared ?

A
8 plus 12 i
B
20 plus 48 i
C
negative 20 plus 48 i
D
16 minus 36 i
14

The polynomial function f of x is equal to 3 x to the 5th power minus 2 x squared plus 7 x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground level? Begin by factoring x to create a constant term.

A
0 , plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
B
plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , plus or minus 3
C
0 , plus or minus 1 seventh , plus or minus 1 , plus or minus 3 sevenths , 3
D
plus or minus 1 third , plus or minus 1 , plus or minus 7 thirds , plus or minus 7
15

Which equation is an example of the commutative property of multiplication?

A
open paren 4 plus 2 i close paren is equal to open paren 4 plus 2 i plus 0 close paren
B
open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren is equal to open paren 3 minus 5 i close paren times open paren 4 plus 2 i close paren
C
open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren is equal to open paren 4 plus 2 i close paren times open paren 3 minus 5 i close paren times 1
D
open paren 4 plus 2 i close paren is equal to open paren 2 i plus 4 close paren
16

If the discriminant of a quadratic equation is 4, which statement describes the roots?

A
There is one real root.
B
There are two complex roots.
C
There are two real roots.
D
There is one complex root.
17

Which equation is y is equal to negative 6 x squared plus 3 x plus 2 rewritten in vertex form?

A
y is equal to negative 6 times open paren x minus 1 half close paren squared plus 7 halves
B
y is equal to negative 6 times open paren x minus 1 fourth close paren squared plus 19 eighths
C
y is equal to negative 6 times open paren x minus 1 close paren squared plus 8
D
y is equal to negative 6 times open paren x plus 1 fourth close paren squared plus 13 eighths
18

What is the greatest possible integer value of x for which square root of x minus 5 end root is an imaginary number?

A
6
B
4
C
5
D
3
19

Which is the approximate length of the longest side of Sandbox 2 ? Round the answer to the nearest hundredth of a meter.

A
10 point 1 8 meters
B
3 point 0 6 meters
C
2 point 7 2 meters
D
9 point 1 6 meters
20

Which point shows the location of 5 minus 2 i on the complex plane?

A
point cap b
B
point cap c
C
point cap A
D
point cap d

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