Answers Algebra II Honors AThe Cube Root Function

The Cube Root Function — Unit test Answers

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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).

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

y = 9 (x + one-half) squared minus thirteen-fourths

y = 9 (x + one-half) squared minus 1

y = 9 (x + one-half) squared + five-fourths

y = 9 (x + one-half) squared minus five-fourths

In which quadrant is the number 6 – 8i located on the complex plane?

III

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

m greater-than StartFraction 25 Over 3 EndFraction

m less-than StartFraction 25 Over 3 EndFraction

m less-than StartFraction 49 Over 12 EndFraction

m greater-than StartFraction 49 Over 12 EndFraction

The solid graph is a translation of .

2 units up

2 units down

2 units left

2 units right

A box is to be constructed with a rectangular base and a height of 5 cm. If the rectangular base must have a perimeter of 28 cm, which quadratic equation best models the volume of the box? V = lwhP = 2(l + w)

y = 5(28 – x)(x)

y = 5(28 – 2x)(x)

y = 5(14 – x)(x)

y = 5(14 – 2x)(x)

Which expression demonstrates the use of the commutative property of addition in the first step of simplifying the expression (–1 + i) + (21 + 5i)?

(–1 + i) + (21 + 5i) + 0

–1 + (i + 21) + 5i

(–1 + 21) + (i + 5i)

–(1 – i) + (21 + 5i)

The sum of two complex numbers, where the real numbers do not equal zero, results in a sum of 34i. Which statement must be true about the complex numbers?

The complex numbers have equal imaginary parts.

The complex numbers have equal real parts.

The complex numbers have opposite imaginary parts.

The complex numbers have opposite real parts.

The graph below shows the height of a projectile t seconds after it is launched. If acceleration due to gravity is –16 ft/s2, which equation models the height of the projectile correctly?h(t) = at2 + vt + h0

h(t) = –16t2 + 42t + 5

h(t) = –16t2 + 5

h(t) = –16t2 + 32

h(t) = –16t2 + 32t + 5

What is the absolute value of the complex number ?

StartRoot 14 EndRoot

3 StartRoot 2 EndRoot

Use completing the square to solve for in the equation .

x = –1 or 15

x = 1 or 7

x = 4 plus-or-minus StartRoot 41 EndRoot

x = 4 plus-or-minus StartRoot 73 EndRoot

The length of a rectangle is three times the width. The area of the rectangle is 108 sq in. What is the width of the rectangle?

6 in.

9 in.

12 in.

36 in.

Use the zero product property to find the solutions to the equation x2 + x – 30 = 12.

x = –7 or x = 6

x = –7 or x = –6

x = –6 or x = 7

x = 6 or x = 7

If x2 + mx + m is a perfect-square trinomial, which equation must be true?

x2 + mx + m = (x – 1)2

x2 + mx + m = (x + 1)2

x2 + mx + m = (x + 2)2

x2 + mx + m = (x + 4)2

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

The discriminant is less than 0, so there are two real roots.

The discriminant is greater than 0, so there are two real roots.

The discriminant is less than 0, so there are two complex roots.

The discriminant is greater than 0, so there are two complex roots.

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

6 units left and 9 units down

6 units right and 9 units down

6 units left and 9 units up

6 units right and 9 units up

A projectile is fired straight up from ground level with an initial velocity of 112 ft/s. Its height, h, above the ground after t seconds is given by h = –16t2 + 112t. What is the interval of time during which the projectile's height exceeds 192 feet?

3 < t < 4

t < 4

t > 4

3 > t > 4

When a baseball is hit by a batter, the height of the ball, h(t), at time t, , is determined by the equation . If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?