AnswersMO-Algebra II AModeling with Systems

Modeling with Systems — Unit test Answers

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Organizers of the town fair make a total of $706 from selling 164 hot dogs and 74 hamburgers at one of their concession stands. At their other concession stand, they make $884 by selling 256 hot dogs and 61 hamburgers. If the prices are the same at both concession stands, what is the price of a hot dog?

A
$0.40
B
$2.50
C
$3.75
D
$4.00
2
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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
3

Which equation represents a graph with a vertex at (1, –6)?

A
y = 3x2 + 6x – 3
B
y = 3x2 – 6x – 3
C
y = 3x2 – 8x – 1
D
y = 3x2 – 3x – 6
4

Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?

A
mc007-1.jpg
Option A
B
mc007-2.jpg
Option B
C
mc007-3.jpg
Option C
D
mc007-4.jpg
Option D
5

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
6

Tim throws a stick straight up in the air from the ground. The function h = –16t2 + 48t models the height, h, in feet, of the stick above the ground after t seconds. Which inequality can be used to find the interval of time in which the stick reaches a height of more than 8 feet?

A
–16t2 + 48t > 8
B
–16t2 + 48t < 8
C
–16t2 + 48t ³ 8
D
–16t2 + 48t £ 8
7

For what values of m does the graph of y = mx2 – 5x – 2 have no x-intercepts?

A
m greater-than negative StartFraction 25 Over 8 EndFraction
Option A
B
m less-than negative StartFraction 25 Over 8 EndFraction
Option B
C
m less-than StartFraction 25 Over 8 EndFraction
Option C
D
m greater-than StartFraction 25 Over 8 EndFraction
Option D
8

Louis used a quadratic equation to model the height, y, of a falling object x seconds after it is dropped. Which ordered pair generated by this model should be discarded because the values are unreasonable?

A
(–4, 1)
B
Option
Option B
C
Option
Option C
D
(6, 0)
9

During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = –16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

A
the height of the bird and the ball when the ball and the bird are the same distance from the player
B
the height of the bird and the ball when the player hits the ball
C
the time when the height of the ball and the bird are the same
D
the time when the ball and the bird hit the ground
11

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

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
13

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = –0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = –0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

A
the height at which the pumpkins reach their greatest horizontal distance from the launch site
B
the horizontal distance of the pumpkins from the launch site when they reach the ground
C
the starting height of the pumpkins when they are at the launch site
D
the horizontal distance of the pumpkins from the launch site when their heights are the same
14

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

A
There are two complex roots.
B
There are two real roots.
C
There is one real root.
D
There is one complex root.
15

What is the sum of 12 – 5i and –3 + 4i?

A
–16 + 63i
B
9 – i
C
9 – 9i
D
15 – 9i
16

Solve for in the equation .

Question illustration
A
x = 3 plus-or-minus StartRoot 23 EndRoot
Option A
B
x = 3 plus-or-minus StartRoot 51 EndRoot
Option B
C
x = 3 plus-or-minus StartRoot 41 EndRoot
Option C
D
x = 3 plus-or-minus StartRoot 5 EndRoot
Option D
17

Which equation is y = –6x2 + 3x + 2 rewritten in vertex form?

A
y = negative 6 (x minus 1) squared + 8
Option A
B
y = negative 6 (x + one-fourth) squared + thirteen-eighths
Option B
C
y = negative 6 (x minus one-fourth) squared + nineteen-eighths
Option C
D
y = negative 6 (x minus one-half) squared + seven-halves
Option D
18

Solve for in the equation .

Question illustration
A
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
Option A
B
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
Option B
C
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option C
D
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
Option D
19

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
20

When graphed, which parabola opens downward?

A
y = –3x2
B
y = (x – 3)2
C
y = one-third x squared
Option C
D
y = x2 – 3
21

A graph of a quadratic function y = f(x) is shown below.What is the solution set of the quadratic inequality f(x) 0?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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