AnswersCommon Core Math III AModeling with Quadratic Equations

Modeling with Quadratic Equations — Unit test Answers

37 verified answers8 views
21
Free Preview

Which statements correctly describe the graph of the function f(x) = x3 – 2x2 – 19x + 20? Select three options.

Question illustration
A
As the x-values increase, the y-values always increase.
B
As x approaches negative infinity, y approaches negative infinity.
C
The domain of the function is all real numbers.
D
The range of the function is y 20.
Option D
E
The graph has a positive y-intercept.
22
Free Preview

The parent function f(x) = x3 and a translation, g(x), are shown on the graph.

Question illustration
A
g(x) = (x + 4)3 + 6
B
g(x) = (x – 4)3 + 6
C
g(x) = (x + 6)3 – 4
D
g(x) = (x – 6)3 – 4
23

The function s(V) = describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters.What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?

Question illustration
A
s > 0
B
s 4
Option B
C
s 8
Option C
D
s 16
Option D
24

Which best describes the graph of the cubic function f(x) = x3 + x2 + x + 1?

A
As x increases, y increases along the entire graph.
B
As x increases, y increases, decreases, and then increases again.
C
As x increases, y decreases, increases, and then decreases again.
D
As x increases, y decreases along the entire graph.
25

The function f(x) = is reflected over the x-axis to create the graph of g(x) = .Which is the graph of g(x)?

Question illustration
A
On a coordinate plane, a cube root function goes through (negative 2, negative 8), has an inflection point at (0, 0), and goes through (2, 8).
Option A
B
On a coordinate plane, a cube root function goes through (negative 2, 8), has an inflection point at (0, 0), and goes through (2, negative 8).
Option B
C
On a coordinate plane, a cube root function goes through (negative 8, 2), has an inflection point at (0, 0), and goes through (8, negative 2).
Option C
D
On a coordinate plane, a cube root function goes through (negative 8, negative 2), has an inflection point at (0, 0), and goes thorugh (8, 2).
Option D
26

The graph of the parent function f(x) = x3 is transformed such that . Which statements about the graph of g(x) are accurate? Select three options.

Question illustration
A
The graph does not pass through the origin.
B
As x approaches negative infinity, the graph of g(x) approaches infinity.
C
As x approaches infinity, the graph of g(x) approaches infinity.
D
The domain of the function is all real numbers.
E
The range of the function is all real numbers.
27

Which is the graph of the function f(x) = 2x3 – 7x2 + 2x + 3?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
28

Which statement about is true?

Question illustration
A
x = –3 is a true solution.
B
x = –3 is an extraneous solution.
C
x = 9 is a true solution.
D
x = 9 is an extraneous solution.
29

The graph of the parent function f(x) = x3 is transformed such that g(x) = f(–2x3). How does the graph of g(x) compare to the graph of f(x)?

A
g(x) is stretched horizontally and reflected over the y-axis.
B
g(x) is stretched horizontally and reflected over the x-axis.
C
g(x) is compressed horizontally and reflected over the y-axis.
D
g(x) is compressed horizontally and reflected over the x-axis.
30

What is the solution to the equation ?

Question illustration
A
x = –12
B
x = –4
C
x = 4
D
x = 12
31

Which equation shows a valid, practical step in solving ?

Question illustration
A
mc006-2.jpg
Option A
B
mc006-3.jpg
Option B
C
mc006-4.jpg
Option C
D
mc006-5.jpg
Option D
32

Which of the following occurs within the solution process for ?

Question illustration
A
squaring both sides once
B
squaring both sides twice
C
cubing both sides once
D
cubing both sides twice
33

Which equation results from isolating a radical term and squaring both sides of the equation for the equation ?

Question illustration
A
mc009-2.jpg
Option A
B
mc009-3.jpg
Option B
C
mc009-4.jpg
Option C
D
mc009-5.jpg
Option D
34

The graph of g(x) is a translation of y = .

Question illustration
A
g(x) =
Option A
B
g(x) =
Option B
C
g(x) =
Option C
D
g(x) =
Option D
35

What is the solution to the equation ? Assume the range is all real numbers.

Question illustration
A
x = –6
B
x = 5
C
x = 6, x = –5
D
x = –6, x = 5
36

Which comparison of the two equations is accurate?Equation A: Equation B:

Question illustration
A
Both equations have different solutions because the square root of a number is not the same as the cube root of a number.
B
Both equations result in different equations after eliminating the radicals, so they have the different solutions.
C
Both equations have the same potential solutions, but equation A might have extraneous solutions.
D
Both equations have the same potential solutions, but equation B might have extraneous solutions.
37

What is the solution to the equation ?

Question illustration
A
n = 2
B
n = 4
C
n = 7
D
n = 14

Did you find these answers helpful?

More from this Course

Quiz
41 verified answers

Unit Test

Quiz
31 verified answers

Unit Test

Quiz
24 verified answers

Test