Answers SS4 PGCPS ALGEBRA 2 OC SUMMER 2027 - 793033Radical Equations and Extraneous Roots

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

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction

y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction

y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds

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Which of the following is the graph of ?

On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4. It starts at x = 3.

On a coordinate plane, an absolute value curve opens down and to the left in quadrants 1 and 2. It starts at x = 3.

On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2. It starts at x = negative 3.

On a coordinate plane, an absolute value curve opens up and to the right in quadrants 3 and 4. It starts at x = negative 3.

The solid graph is a translation of .

2 units up

2 units down

2 units left

2 units right

If the range of and the range of are the same, which statement is true about the value of m?

m can only equal 1.

m can be any positive real number.

m can be any negative real number.

m can be any real number.

What is the following quotient?

StartFraction StartRoot 3 EndRoot Over 4 EndFraction

StartFraction 1 + StartRoot 3 EndRoot Over 4 EndFraction

StartFraction 1 minus StartRoot 3 EndRoot Over 4 EndFraction

StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction

What is the following simplified product? Assume

10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot

11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot

10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot

11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot

Which statement is true of the function f(x) = ? Select three options.The function is always increasing.The function has a domain of all real numbers.The function has a range of {y|– < y < }.The function is a reflection of y = .The function passes through the point (3, –27).

The function is always increasing.

The function has a domain of all real numbers.

The function has a range of {y|– < y < }.

The function is a reflection of y = .

The function passes through the point (3, –27).

The formula gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches?

in.

The speed that a tsunami can travel is modeled by the equation , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers. What is the approximate depth of water for a tsunami traveling at 200 kilometers per hour?

0.32 km

0.75 km

1.12 km

3.17 km

What is the solution of ?

x = –3

x = 4

x = –3 or x = 4

no solution

Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is the approximate value of the account after 2.5 years?

$6,075

$6,118

$6,456

$6,778

What is the following sum?

7 x (RootIndex 6 StartRoot x squared y EndRoot)

7 x squared (RootIndex 6 StartRoot x y squared EndRoot)

7 x squared (RootIndex 3 StartRoot x y squared EndRoot)

7 x (RootIndex 3 StartRoot x squared y EndRoot)

What is the following quotient?

StartFraction StartRoot 3 EndRoot Over 4 EndFraction

StartFraction 1 + StartRoot 3 EndRoot Over 4 EndFraction

StartFraction 1 minus StartRoot 3 EndRoot Over 4 EndFraction

StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction

What is the following product?

x squared (RootIndex 3 StartRoot 28 x squared EndRoot)

x Superscript 5 Baseline (RootIndex 3 StartRoot 28 x EndRoot)

4 x squared (RootIndex 3 StartRoot 3 x squared EndRoot)

4 x Superscript 5 Baseline (RootIndex 3 StartRoot 3 x EndRoot)

What is the solution of ?

x = 142

x = 232

x = 322

no solution

0.32 km

0.75 km

1.12 km

3.17 km

What is the following sum?

7 x (RootIndex 6 StartRoot x squared y EndRoot)

7 x squared (RootIndex 6 StartRoot x y squared EndRoot)

7 x squared (RootIndex 3 StartRoot x y squared EndRoot)

7 x (RootIndex 3 StartRoot x squared y EndRoot)

Which function has the domain ?

y = StartRoot x + 11 EndRoot + 5

y = StartRoot x minus 11 EndRoot + 5

y = StartRoot x + 5 EndRoot minus 11

y = StartRoot x + 5 EndRoot + 11

Which expression is equivalent to ?

216

1,728

RootIndex 3 StartRoot 12 EndRoot

RootIndex 3 StartRoot 72 EndRoot

What is the following product?

2 StartRoot 10 EndRoot

3 StartRoot 10 EndRoot

4 StartRoot 10 EndRoot

10 StartRoot 3 EndRoot

Which describes how to graph by transforming the parent function?

Translate the parent function 5 units to the left and 7 units up.

Translate the parent function 5 units to the right and 7 units up.

Translate the parent function 5 units down and 7 units to the right.

Translate the parent function 5 units up and 7 units to the right.

Which expression is equivalent to ?

StartFraction RootIndex 4 StartRoot 200 EndRoot Over 2 EndFraction

StartFraction RootIndex 4 StartRoot 20 EndRoot Over 2 EndFraction

StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction

StartFraction 100 Over 8 EndFraction

Which expression is equivalent to ?

StartFraction RootIndex 4 StartRoot 200 EndRoot Over 2 EndFraction

StartFraction RootIndex 4 StartRoot 20 EndRoot Over 2 EndFraction

StartFraction 2 StartRoot 5 EndRoot Over 5 EndFraction

StartFraction 100 Over 8 EndFraction

The graph of the cube root parent function y = is translated to form f(x) shown on the graph.

f(x) =

The graph of the cube root parent function y = is translated to form f(x) shown on the graph.

f(x) =

Which of the following describes the graph of compared to the parent cube root function?

stretched by a factor of 2 and translated 64 units right and 5 units down

stretched by a factor of 8 and translated 8 units right and 5 units down

stretched by a factor of 2 and translated 8 units right and 5 units down

stretched by a factor of 8 and translated 64 units right and 5 units down

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

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 9 EndFraction

y = plus-or-minus StartRoot StartFraction x Over 9 EndFraction + 4 EndRoot

y = StartFraction plus-or-minus StartRoot x + 4 EndRoot Over 3 EndFraction

y = StartFraction plus-or-minus StartRoot x EndRoot Over 3 EndFraction + two-thirds

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 the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?

2 Superscript one-third

2 Superscript one-half

2 Superscript two-thirds

2 Superscript three-halves

in.

Which expression is equivalent to ?

216

1,728

RootIndex 3 StartRoot 12 EndRoot

RootIndex 3 StartRoot 72 EndRoot

Which function has the domain ?

y = StartRoot x + 11 EndRoot + 5

y = StartRoot x minus 11 EndRoot + 5

y = StartRoot x + 5 EndRoot minus 11

y = StartRoot x + 5 EndRoot + 11

Which of the following is the graph of ?

On a coordinate plane, an absolute value curve opens up and to the right in quadrant 4. It starts at x = 3.

On a coordinate plane, an absolute value curve opens down and to the left in quadrants 1 and 2. It starts at x = 3.

On a coordinate plane, an absolute value curve opens down and to the left in quadrant 2. It starts at x = negative 3.

On a coordinate plane, an absolute value curve opens up and to the right in quadrants 3 and 4. It starts at x = negative 3.

What is the following product?

2 StartRoot 10 EndRoot

3 StartRoot 10 EndRoot

4 StartRoot 10 EndRoot

10 StartRoot 3 EndRoot

What is the following simplified product? Assume

10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot + x squared StartRoot 15 x EndRoot

11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus x Superscript 4 Baseline StartRoot 75 EndRoot + x squared StartRoot 15 EndRoot

10 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x squared StartRoot 15 EndRoot

11 x Superscript 4 Baseline StartRoot 6 EndRoot + x cubed StartRoot 30 x EndRoot minus 10 x Superscript 4 Baseline StartRoot 3 EndRoot minus x cubed StartRoot 15 x EndRoot

Kaylib’s eye-level height is 48 ft above sea level, and Addison’s eye-level height is ft above sea level. How much farther can Addison see to the horizon? Use the formula , with d being the distance they can see in miles and h being their eye-level height in feet.

What is the following product? Assume

80 x Superscript 4 Baseline + 8 x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x Superscript 4

80 x Superscript 6 Baseline + 8 x Superscript 5 Baseline + 8 x Superscript 5 Baseline StartRoot 30 EndRoot + 24 x Superscript 4

104 x Superscript 4

104 x Superscript 4 + 16 x Superscript 4 Baseline StartRoot 30 EndRoot

The function is always increasing.

The function has a domain of all real numbers.

The function has a range of {y|– < y < }.

The function is a reflection of y = .

The function passes through the point (3, –27).

Which equation is the inverse of ?

y = one-sixth x squared minus four-thirds x + StartFraction 43 Over 9 EndFraction

y = 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

y = negative 4 plus-or-minus StartRoot 6 x minus StartFraction 34 Over 3 EndFraction EndRoot

negative (x minus 4) squared minus two-thirds = negative 6 y + 12

Which expression is equivalent to ?

StartFraction RootIndex 12 StartRoot 27 EndRoot Over 2 EndFraction

StartFraction RootIndex 4 StartRoot 24 EndRoot Over 2 EndFraction

StartFraction RootIndex 12 StartRoot 55296 EndRoot Over 2 EndFraction

StartFraction RootIndex 12 StartRoot 177147 EndRoot Over 3 EndFraction

Mario invested $6,000 in an account that pays 5% annual interest compounded annually. Using the formula A = P(1 + r)t, what is the approximate value of the account after 2.5 years?

$6,075

$6,118

$6,456

$6,778

What is the simplified form of the following expression?

6 StartRoot 2 EndRoot

18 StartRoot 2 EndRoot

30 StartRoot 2 EndRoot

36 StartRoot 2 EndRoot

What is the domain of the function ?

x greater-than-or-equal-to negative 5

x greater-than-or-equal-to 2

x greater-than-or-equal-to 5

x greater-than-or-equal-to 10

The solid graph is a translation of .

2 units up

2 units down

2 units left

2 units right

If the range of and the range of are the same, which statement is true about the value of m?

m can only equal 1.

m can be any positive real number.

m can be any negative real number.

m can be any real number.

What is the following quotient?

StartFraction 9 StartRoot 7 EndRoot + StartRoot 14 EndRoot Over negative 3 EndFraction

StartFraction 36 minus 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot minus StartRoot 14 EndRoot EndFraction

StartFraction 36 + 9 StartRoot 7 EndRoot + 4 StartRoot 2 EndRoot + StartRoot 14 EndRoot Over 9 EndFraction

StartFraction 79 Over 9 EndFraction

Which describes how to graph by transforming the parent function?

Translate the parent function 5 units to the left and 7 units up.

Translate the parent function 5 units to the right and 7 units up.

Translate the parent function 5 units down and 7 units to the right.

Translate the parent function 5 units up and 7 units to the right.

What is the following product? Assume

80 x Superscript 4 Baseline + 8 x Superscript 4 Baseline StartRoot 30 x EndRoot + 24 x Superscript 4

80 x Superscript 6 Baseline + 8 x Superscript 5 Baseline + 8 x Superscript 5 Baseline StartRoot 30 EndRoot + 24 x Superscript 4

104 x Superscript 4

104 x Superscript 4 + 16 x Superscript 4 Baseline StartRoot 30 EndRoot

Which function is undefined for x = 0?

y = RootIndex 3 StartRoot x minus 2 EndRoot

y = StartRoot x minus 2 EndRoot

y = RootIndex 3 StartRoot x + 2 EndRoot

y = StartRoot x + 2 EndRoot

Which function is undefined for x = 0?

y = RootIndex 3 StartRoot x minus 2 EndRoot

y = StartRoot x minus 2 EndRoot

y = RootIndex 3 StartRoot x + 2 EndRoot

y = StartRoot x + 2 EndRoot

What is the simplified form of the following expression?

6 StartRoot 2 EndRoot

18 StartRoot 2 EndRoot

30 StartRoot 2 EndRoot

36 StartRoot 2 EndRoot

The orbital period, P, of a planet and the planet’s distance from the sun, a, in astronomical units is related by the formula . If Saturn’s orbital period is 29.5 years, what is its distance from the sun?

9.5 AU

19.7 AU

44.3 AU

160.2 AU

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