Answers717- Algebra II AModeling with Systems

Modeling with Systems — Cumulative exam Answers

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When graphed, which parabola opens downward?

Question illustration
y
y = –3x2
y
y = (x – 3)2
C
Option
Option C
y
y = x2 – 3
62
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Rene is designing a satellite that is the shape of a parabola that opens upward with a diameter of 8 in. and a depth of 2 in. The feed antenna focuses the incoming radio waves. At what point should the feed antenna be placed?

A
(–8, 0)
B
(–2, 0)
C
(0, 2)
D
(0, 8)
63

What values of c and d make the equation true? Assume and

Question illustration
A
c = 1, d = 3
B
c = 1, d = 9
C
c = 2, d = 8
D
c = 2, d = 9
64

The graph of f(x) is shown below.If g(x) and f(x) are inverse functions, which graph represents g(x)?

Question illustration
A
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up sharply through (2, 4).
Option A
B
On a coordinate plane, a curve opens down and to the left in quadrant 2. The curve starts at (0, 0) and gradually curves through (negative 4, 2).
Option B
C
On a coordinate plane, a curve opens open and to the left in quadrant 3. The curve starts at (0, 0) and curves gradually through (negative 4, negative 2).
Option C
D
On a coordinate plane, a curve opens up and to the left in quadrant 1. The curve starts at (0, 0) and curves up through (4, 1).
Option D
65

Gabriella is designing a flashlight that uses a parabolic reflecting mirror and a light source. The shape of the mirror can be modeled by where x and y are measured in inches. Where should she place the bulb to ensure a perfect beam of light?

Question illustration
A
6.5 in. to the left of the vertex
B
6.5 in. above the vertex
C
6.5 in. to the right of the vertex
D
6.5 in. below the vertex
66

Which expression shows the sum of the polynomials with like terms grouped together?

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
mc004-4.jpg
Option C
D
mc004-5.jpg
Option D
67

The equation shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If planet Y is k times the mean distance from the sun as planet X, by what factor is the orbital period increased?

Question illustration
A
k Superscript one-third
Option A
B
k Superscript one-half
Option B
C
k Superscript two-thirds
Option C
D
k Superscript three-halves
Option D
68

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of ?

Question illustration
A
mc016-2.jpg
Option A
B
mc016-3.jpg
Option B
C
mc016-4.jpg
Option C
D
mc016-5.jpg
Option D
69

What is the completely factored form of ?

Question illustration
A
(2x - 5)(3x + 1)
B
(2x + 5)(3x - 1)
C
(2x - 1)(3x - 5)
D
(2x + 1)(3x + 5)
70

What are the domain and range of the function below?

Question illustration
A
domain: range:
Option A
B
domain: range:
Option B
C
domain: range:
Option C
D
domain: range:
Option D
71

Which classification describes the following system of equations?

Question illustration
A
inconsistent and dependent
B
consistent and dependent
C
consistent and independent
D
inconsistent and independent
72

What is one solution of the following system?

Question illustration
A
(–6, 0)
B
(–2, 4)
C
(0, –6)
D
(4, –2)
73

Which function is the inverse of ?

Question illustration
A
f Superscript negative 1 Baseline (x) = negative one-fifth x + four-fifths
Option A
B
mc014-3.jpg
Option B
C
mc014-4.jpg
Option C
D
mc014-5.jpg
Option D
74

Which quadratic inequality does the graph below represent?

Question illustration
A
mc012-2.jpg
Option A
B
mc012-3.jpg
Option B
C
mc012-4.jpg
Option C
D
mc012-5.jpg
Option D
75

Which statement verifies that f(x) and g(x) are inverses of each other?

A
mc016-1.jpg
Option A
B
and
Option B
C
mc016-4.jpg
Option C
D
and
Option D
76

A cable company wants to provide cell phone service for residents on an island. The function for the cost of laying the cable from the island to the mainland is , where x represents the length of the cable in meters. What are the domain and range of the function?

Question illustration
A
domain: all real numbers range: all real numbers greater than or equal to 17,000
B
domain: all real numbers greater than or equal to 0range: all real numbers greater than or equal to 17,000
C
domain: all real numbers greater than or equal to 0range: all real numbers greater than or equal to 13,000
D
domain: all real numbers greater than or equal to 13,000range: all real numbers greater than or equal to 0
77

Which expression is equivalent to ? Assume and .

Question illustration
A
StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 2 c cubed EndFraction
Option A
B
StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a squared c cubed EndFraction
Option B
C
StartFraction a cubed b (RootIndex 3 StartRoot 15 b squared EndRoot) Over 6 c cubed EndFraction
Option C
D
StartFraction b (RootIndex 3 StartRoot 15 b EndRoot) Over 2 a c EndFraction
Option D
78

The table below shows the data for a car stopping on a wet road. What is the approximate stopping distance for a car traveling 35 mph? Car Stopping Distancesv(mph)d(ft)1517.92031.850198.7

Question illustration
A
41.7 ft
B
49.7 ft
C
97.4 ft
D
115.3 ft
79

Which statement is true about ?

Question illustration
A
The graph of f(x) has a vertex of (–3, 2).
B
The graph of f(x) is a horizontal compression of the graph of the parent function.
C
The graph of f(x) opens downward.
D
The graph of f(x) has range of f(x) –2.
Option D
80

What are the values of x in the equation x2 – 6x + 9 = 25?

A
x = –2 or x = 8
B
x = –1 or x = –11
C
x = 1 or x = 11
D
x = 2 or x = –8

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