Answers Advanced Algebra Concepts and Connections_TC_Online LearningUnit Test

Unit Test — Unit test Answers

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The graph of a quadratic inequality is shown.

y greater-than 3 (x + 15)(x + 3)

y greater-than-or-equal-to (x + 15)(x + 3)

y greater-than 0.25 (x minus 15)(x minus 3)

y greater-than-or-equal-to (x minus 15)(x minus 3)

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A company’s profit is modeled by the quadratic function with zeros 6 and 42. The point (15, 81) is on the boundary line. Any values above the boundary line exceed the expected profits.

y less-than one-third x squared + 16 x minus 84

y greater-than negative one-third x squared + 16 x minus 84

y less-than negative one-third x squared + 16 x minus 84

y greater-than one-third x squared minus 16 x + 84

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.

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

y = 4x2 + 24x + 38

y = 4x2 – 24x + 38

y = 4x2 + 12x + 2

y = 4x2 + 16x + 13

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

Which equation demonstrates the multiplicative identity property?

(negative 3 + 5 i) + 0 = negative 3 + 5 i

(negative 3 + 5 i ) (1) = negative 3 + 5 i

(negative 3 + 5 i) (negative 3 + 5 i) = negative 16 minus 30 i

(negative 3 + 5 i) (3 minus 5 i) = 16 + 30 i

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)

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

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

y = –(x + 7)2 + 7

y = (x – 7)2 – 7

y = (x – 7)2 + 7

y = (x – 7)2

Which values of x and y would make the following expression represent a real number?(4 + 5i)(x + yi)

x = 4, y = 5

x = –4, y = 0

x = 4, y = –5

x = 0, y = 5

A quadratic inequality contains the values less than or equal to the quadratic function that has a vertex of (–9, –27) and contains the point on the boundary.

y less-than-or-equal-to two-thirds (x minus 9) squared + 27

y less-than-or-equal-to negative two-thirds (x minus 9) squared + 27

y less-than-or-equal-to two-thirds (x + 9) squared minus 27

y less-than-or-equal-to negative two-thirds (x + 9) squared minus 27

The graph represents the projected profits for a company, y, based on the number of units sold, x.

y less-than negative 2 (x + 25) squared minus 200

y greater-than 2 (x minus 25) squared + 200

y greater-than 2 (x + 25) squared minus 200

y less-than minus 2 (x minus 25) squared + 200

Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3?

2 units left and 3 units up

2 units left and 3 units down

2 units right and 3 units up

2 units right and 3 units down

How does the graph of y = a(x – h)2 + k change if the value of h is doubled?

The vertex of the graph moves to a point twice as far from the x-axis.

The vertex of the graph moves to a point twice as far from the y-axis.

The vertex of the graph moves to a point half as far from the x-axis.

The vertex of the graph moves to a point half as far from the y-axis.

On a coordinate plane, a parabola with a dashed boundary line opens up. It goes through (negative 1, 0), has a vertex at (1, negative 16), and goes through (3, 0).

y less-than 4 (x minus 1) squared minus 11

y less-than negative 4 (x minus 1) squared minus 11

y less-than 4 (x minus 1) squared minus 16

On a coordinate plane, a parabola with a dashed boundary line opens up. It goes through (negative 1, 0), has a vertex at (1, negative 16), and goes through (3, 0).

Which phrase best describes the translation from the graph y = 2(x – 15)2 + 3 to the graph of y = 2(x – 11)2 + 3?

4 units to the left

4 units to the right

8 units to the left

8 units to the right

Which equation has a graph that is a parabola with a vertex at (–2, 0)?

y = –2x2

y = (x + 2)2

y = (x – 2)2

y = x2 – 2

Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x.

commutative property

identity property

distributive property

associative property

Which inequality in vertex form represents the region less than or equal to the quadratic function with vertex (–6, 12) and includes the point (–9, 15) on the boundary?

y less-than-or-equal-to one-third (x minus 6) squared + 12

y less-than-or-equal-to one-third (x + 6) squared + 12

y less-than-or-equal-to 3 (x + 6) squared + 12

y less-than-or-equal-to 3 (x minus 6) squared + 12

Which equation has a graph that is a parabola with a vertex at (–1, –1)?

y = (x – 1)2 + 1

y = (x – 1)2 – 1

y = (x + 1)2 + 1

y = (x + 1)2 – 1

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