AnswersCommon Core Math III ASquare Root Functions

Square Root Functions — Unit test Answers

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What is one of the solutions to the following system?

Question illustration
A
(–5, 2)
B
(–2, 1)
C
(2, 5)
D
(8, 5)
2
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Which statement about the following equation is true?2x2 – 9x + 2 = –1

A
The discriminant is less than 0, so there are two real roots.
B
The discriminant is less than 0, so there are two complex roots.
C
The discriminant is greater than 0, so there are two real roots.
D
The discriminant is greater than 0, so there are two complex roots.
3

Which equation is the inverse of ?

Question illustration
A
y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction
Option A
B
y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot
Option B
C
y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot
Option C
D
negative (x minus 4) squared minus two-thirds = negative 6 y + 12
Option D
4

Which equation has a graph that lies entirely above the x-axis?

A
y = –(x + 7)2 + 7
B
y = (x – 7)2 – 7
C
y = (x – 7)2 + 7
D
y = (x – 7)2
5

Which phrase best describes the translation from the graph y = (x – 5)2 + 7 to the graph of y = (x + 1)2 – 2?

A
6 units left and 9 units down
B
6 units right and 9 units down
C
6 units left and 9 units up
D
6 units right and 9 units up
6

Using the quadratic formula to solve 4x2 – 3x + 9 = 2x + 1, what are the values of x?

A
StartRoot 1 plus-or-minus StartRoot 159 EndRoot i Over 8 EndFraction
Option A
B
StartRoot 5 plus-or-minus StartRoot 153 EndRoot i Over 8 EndFraction
Option B
C
StartRoot 5 plus-or-minus StartRoot 103 EndRoot i Over 8 EndFraction
Option C
D
StartRoot 1 plus-or-minus StartRoot 153 EndRoot Over 8 EndFraction
Option D
7

Which system is equivalent to ?

Question illustration
A
StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row 12 x squared + 4 y squared = 22 EndLayout
Option A
B
StartLayout Enlarged left-brace 1st Row 3 x squared minus 4 y squared = 25 2nd row negative 12 x squared + 4 y squared = 22 EndLayout
Option B
C
StartLayout Enlarged left-brace 1st Row 6 x squared minus 8 y squared = 25 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout
Option C
D
StartLayout Enlarged left-brace 1st Row 6 x squared minus 8 y squared = 50 2nd row negative 6 x squared minus 2 y squared = 11 EndLayout
Option D
8

What is the domain of the function ?

Question illustration
A
x greater-than-or-equal-to negative 5
Option A
B
x greater-than-or-equal-to 2
Option B
C
x greater-than-or-equal-to 5
Option C
D
x greater-than-or-equal-to 10
Option D
9

The center of a circle is at the origin on a coordinate grid. A line with a positive slope intersects the circle at (0, 7). Which statement must be true?

A
The circle has a radius greater than 7.
B
The circle has a radius equal to 7.
C
The slope of the line is equal to 7.
D
The slope of the line is not equal to 7.
10

Which function has the domain ?

Question illustration
A
y = StartRoot x + 11 EndRoot + 5
Option A
B
y = StartRoot x minus 11 EndRoot + 5
Option B
C
y = StartRoot x + 5 EndRoot minus 11
Option C
D
y = StartRoot x + 5 EndRoot + 11
Option D
11

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

A
The discriminant is less than 0, so there are two real roots.
B
The discriminant is greater than 0, so there are two real roots.
C
The discriminant is less than 0, so there are two complex roots.
D
The discriminant is greater than 0, so there are two complex roots.
12

The vertex of a parabola that opens downward is at (0, 4). The vertex of a second parabola is at (0, –4). If the parabolas intersect at two points, which statement must be true?

A
The second parabola opens downward.
B
The second parabola opens upward.
C
The points of intersection are on the x-axis.
D
The points of intersection are of equal distance from the y-axis.
13

Which equation is the inverse of y = 9x2 – 4?

A
y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction
Option A
B
y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot
Option B
C
y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction
Option C
D
y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds
Option D
14

Which equation represents a graph with a vertex at (–3, 2)?

A
y = 4x2 + 24x + 38
B
y = 4x2 – 24x + 38
C
y = 4x2 + 12x + 2
D
y = 4x2 + 16x + 13
15

Which equation is y = 9x2 + 9x – 1 rewritten in vertex form?

A
y = 9 (x + one-half) squared minus thirteen-fourths
Option A
B
y = 9 (x + one-half) squared minus 1
Option B
C
y = 9 (x + one-half) squared + five-fourths
Option C
D
y = 9 (x + one-half) squared minus five-fourths
Option D
16

For what values of m does the graph of y = 3x2 + 7x + m have two x-intercepts?

A
m greater-than StartFraction 25 Over 3 EndFraction
Option A
B
m less-than StartFraction 25 Over 3 EndFraction
Option B
C
m less-than StartFraction 49 Over 12 EndFraction
Option C
D
m greater-than StartFraction 49 Over 12 EndFraction
Option D
17

Which equation is part of solving the system by substitution?

Question illustration
A
4(y + 11)2 – 3y2 = 8
B
4(11 – y)2 – 3y2 = 8
C
4(y – 11)2 – 3y2 = 8
D
4(–11y)2 – 3y2 = 8
18

Which equation is the inverse of y = 16x2 + 1?

A
y = plus-or-minus StartRoot StartFraction x Over 16 EndFraction minus 1 EndRoot
Option A
B
y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 16 EndFraction
Option B
C
y = StartFraction plus-or-minus StartRoot x EndRoot Over 4 EndFraction minus one-fourth
Option C
D
y = StartFraction plus-or-minus StartRoot x minus 1 EndRoot Over 4 EndFraction
Option D
19

Which equation is the inverse of ?

Question illustration
A
y = one-fifth x squared + six-fifths x + eleven-tenths
Option A
B
y = 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Option B
C
Negative 5 y minus 4 = negative (x + 3) squared minus one-half
Option C
D
y = negative 3 plus-or-minus StartRoot 5 x + seven-halves EndRoot
Option D
20

What is the domain of the square root function graphed below?

Question illustration
A
x greater-than 1
Option A
B
x greater-than-or-equal-to 10
Option B
C
x greater-than 3
Option C
D
x greater-than-or-equal-to 3
Option D

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