AnswersFL-1200330-Algebra 2 CRTransformations of Quadratic Functions

Transformations of Quadratic Functions — Unit test Answers

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1
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Which expression is equivalent to (4 + 6i)2?

A
–20 + 48i
B
8 + 12i
C
16 – 36i
D
20 + 48i
2
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Susan plans to use 120 feet of fencing to enclose a rectangular area for a garden. Which equation best models the area, y, of the rectangular garden that she creates if one side is x feet long?A = lw

A
y = (60 – x)(x)
B
y = (120 – x)(120 + x)
C
y = (120 – x)(x)
D
y = (60 – x)(60 + x)
3

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
4

An egg is dropped from a height of 90 ft. If acceleration due to gravity is –16 ft/s2 and initial velocity is 0 ft/s, approximately how long will it take for the egg to reach the ground?h(t) = at2 + vt + h0

A
1.9 s
B
2.4 s
C
9.7 s
D
40.7 s
5

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)
6

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

Question illustration
A
point A
B
point B
C
point C
D
point D
7

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)
8

Which is the standard form of the equation of the parabola that has a vertex of (–4, –3) and a directrix of x = 2?

A
mc012-1.jpg
Option A
B
mc012-2.jpg
Option B
C
mc012-3.jpg
Option C
D
mc012-4.jpg
Option D
9

Which equation is y = 3(x – 2)2 – (x – 5)2 rewritten in vertex form?

A
y = 3 (x minus seven-halves) squared minus StartFraction 27 Over 4 EndFraction
Option A
B
y = 2 (x minus 1) squared minus 11
Option B
C
y = 2 (x minus one-half) squared minus StartFraction 53 Over 4 EndFraction
Option C
D
y = 2 (x minus one-half) squared minus StartFraction 27 Over 2 EndFraction
Option D
10

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.
11

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

A
–16 + 63i
B
9 – i
C
9 – 9i
D
15 – 9i
12

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
13

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
14

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

A
(4 + 2i) = (2i + 4)
B
(4 + 2i)(3 – 5i) = (3 – 5i)(4 + 2i)
C
(4 + 2i)(3 – 5i) = (4 + 2i)(3 – 5i)(1)
D
(4 + 2i) = (4 + 2i + 0)
15

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
16

Which pair of complex numbers has a real-number product?

A
(1 + 3i)(6i)
B
(1 + 3i)(2 – 3i)
C
(1 + 3i)(1 – 3i)
D
(1 + 3i)(3i)
17

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
18

What is the value of i 97 – i?

A
–i
B
0
C
–2i
D
i Superscript 96
Option D
19

For which value of m does the graph of y = 18x2 + mx + 2 have exactly one x-intercept?

A
0
B
9
C
12
D
16
20

Using the quadratic formula to solve 11x2 – 4x = 1, what are the values of x?

A
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 15 EndRoot Over 11 EndFraction
Option A
B
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction 2 StartRoot 15 EndRoot Over 11 EndFraction
Option B
C
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot Over 11 EndFraction
Option C
D
StartFraction 2 Over 11 EndFraction plus-or-minus StartFraction StartRoot 7 EndRoot i Over 11 EndFraction
Option D

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