Answers Algebra IIQuadratics and Complex Numbers

Quadratics and Complex Numbers — Test Answers

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Solve for x in the equation x squared minus 8 x plus 41 is equal to 0

x is equal to negative 4 plus or minus 5 i

x is equal to 4 plus or minus 5 i

x is equal to 4 plus or minus square root of 37 i

x is equal to negative 4 plus or minus square root of 37 i

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Which is the graph of the function f of x is equal to x cubed plus x squared plus x plus 1 ?

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis. Both axes are labeled from negative 4 to 4. The curve begins in the third quadrant, with an arrowhead pointing downward near the coordinates negative 1 point 2 comma negative 4. Moving upward and to the right, the curve passes through the grid intersection at negative 1 comma negative 2. The curve crosses the vertical y-axis at the point 0 comma negative 1. From there, the curve turns upward more steeply, crossing the horizontal x-axis between 0 and 1, and passes through the grid intersection at 1 comma 2.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis. Both axes are labeled from negative 4 to 4. The curve begins in the fourth quadrant, with an arrowhead pointing downward near the coordinates negative 1 point 2 comma negative 4. Moving upward and to the right, the curve passes through the grid intersection at negative 1 comma negative 2. It then curves more gradually, crossing the horizontal x-axis between negative 1 and 0, and passes through the vertical y-axis at the point 0 comma 1. From there, the curve turns upward more steeply, passing through the grid intersection at 1 comma 4.

Image with description A coordinate plane with a horizontal x-axis and a vertical y-axis. Both axes are labeled from negative 4 to 4. The curve begins in the fourth quadrant with an arrowhead pointing downward near the coordinates 0 point 5 comma negative 4. Moving upward and to the right, the curve passes through the grid intersection at 1 comma negative 2. It then curves more gradually, flattened near the grid intersection at 2 comma negative 1. From there, the curve turns upward more steeply, crossing the horizontal x-axis between 2 and 3, and passes through the grid intersection at 3 comma 2. It continues upward into the first quadrant, ending with an arrowhead pointing upward near the coordinates 3 point 2 comma 4.

Image with description A coordinate plane displays the x-axis labeled from negative 4 to 4 in increments of 1 and the y-axis labeled from negative 4 to 4 in increments of 1. An increasing curve enters from below near 0.2 comma negative 4, rises steeply, passes through approximately 1 comma 0 and 2 comma 1.

Which equation represents a graph with a vertex at open paren negative 3 comma 2 close paren ?

y is equal to 4 x squared plus 12 x plus 2

y is equal to 4 x squared plus 16 x plus 13

y is equal to 4 x squared minus 24 x plus 38

y is equal to 4 x squared plus 24 x plus 38

Which phrase best describes the translation from the graph y is equal to open paren x minus 5 close paren squared plus 7 to the graph of y is equal to open paren x plus 1 close paren squared minus 2 ?

6 units left and 9 units down

6 units right and 9 units up

6 units left and 9 units up

6 units right and 9 units down

The graph of the parent function f of x is equal to x cubed is translated to form the graph of g of x is equal to x plus 3 cubed minus 4 The point 0 comma 0 on the graph of f of x corresponds to which point on the graph of g of x ?

negative 3 comma negative 4

3 comma 4

3 comma negative 4

negative 3 comma 4

Which equation is the inverse of y is equal to 9 x squared minus 4 ?

y is equal to plus or minus square root of x over 9 plus 4 end root

y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 3

y is equal to the fraction with numerator plus or minus square root of x plus 4 end root and denominator 9

y is equal to the fraction with numerator plus or minus square root of x and denominator 3 plus 2 thirds

The area of a triangle is 1 comma 440 cm squared The base of the triangle is 5 times the height. What is the height of the triangle?

12 cm

24 cm

60 cm

46 cm

Use completing the square to solve for x in the equation open paren x minus 12 close paren times open paren x plus 4 close paren is equal to 9

x is equal to 1 or 7

x is equal to 4 plus or minus square root of 73

x is equal to negative 1 or 15

x is equal to 4 plus or minus square root of 41

What is the domain of the function y is equal to 2 square root of x minus 5 end root ?

x is greater than or equal to 10

x is greater than or equal to negative 5

x is greater than or equal to 5

x is greater than or equal to 2

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

y is equal to open paren x minus 7 close paren squared

y is equal to open paren x minus 7 close paren squared minus 7

y is equal to negative open paren x plus 7 close paren squared plus 7

y is equal to open paren x minus 7 close paren squared plus 7

Solve for x in the equation x squared minus 12 x plus 36 is equal to 90

x is equal to 12 plus or minus 3 square root of 10

x is equal to 6 plus or minus 2 square root of 7

x is equal to 6 plus or minus 3 square root of 10

x is equal to 12 plus or minus 3 square root of 22

Use the zero product property to find the solutions to the equation x squared plus x minus 30 is equal to 12

x is equal to negative 7 or x is equal to 6

x is equal to negative 7 or x is equal to negative 6

x is equal to negative 6 or x is equal to 7

x is equal to 6 or x is equal to 7

Use the zero product property to find the solutions to the equation 6 x squared minus 5 x is equal to 56

x is equal to negative 1 half or x is equal to 56 thirds

x is equal to negative 8 or x is equal to 7 sixths

x is equal to negative 3 sevenths or x is equal to 2 thirds

x is equal to negative 8 thirds or x is equal to 7 halves

The graph of the parent function f of x is equal to x cubed is translated to form g of x is equal to x minus 7 cubed plus 9 Which is the graph of g of x , the translated function?

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A smooth increasing curve passes through approximately the points 1.5 comma negative 5, 2 comma negative 3, 3 comma negative 2, 4 comma 0, and 5 comma 5. The curve becomes steeper as it moves upward and to the right.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A smooth increasing curve begins near the point negative 3 comma negative 5 and rises to approximately 0.5 comma 5. The curve passes through approximately the points negative 2 comma negative 3, negative 1 comma negative 2.5, and 0 comma 1. The curve becomes steeper as it moves upward and to the right.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A smooth increasing curve begins near the point 1 comma negative 5 and rises to approximately 4 comma 5. The curve passes through approximately the points 2 comma negative 3, 3 comma negative 3, and 4 comma 5. The curve becomes steeper as it moves upward and to the right.

Image with description A coordinate plane displays the x-axis labeled from negative 5 to 5 in increments of 1 and the y-axis labeled from negative 5 to 5 in increments of 1. A smooth increasing curve passes through approximately the points negative 4 comma negative 5, negative 3 comma negative 2, negative 2 comma negative 1, negative 1 comma 0, and negative 0.5 comma 5. The curve becomes steeper as it moves upward and to the 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? cap v is equal to l w h cap p is equal to 2 times open paren l plus w close paren

y is equal to 5 open paren 28 minus 2 x close paren x

y is equal to 5 open paren 28 minus x close paren x

y is equal to 5 open paren 14 minus 2 x close paren x

y is equal to 5 open paren 14 minus x close paren x

Stacey has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is 14 the area of the original square. What was the side length of the original square? cap A is equal to s squared

2 in.

6 in.

12 in.

1 in.

If x squared plus m x plus m is a perfect-square trinomial, which equation must be true?

x squared plus m x plus m is equal to open paren x minus 1 close paren squared

x squared plus m x plus m is equal to open paren x plus 2 close paren squared

x squared plus m x plus m is equal to open paren x plus 4 close paren squared

x squared plus m x plus m is equal to open paren x plus 1 close paren squared

A rectangular pan has a length that is 43 the width. The total area of the pan is 432 in.2. What is the width of the cake pan? cap A is equal to l w

18 in.

13 point 9 in.

10 point 4 in.

24 in.

Which function has the domain x is greater than or equal to negative 11 ?

y is equal to square root of x minus 11 end root plus 5

y is equal to square root of x plus 5 end root minus 11

y is equal to square root of x plus 5 end root plus 11

y is equal to square root of x plus 11 end root plus 5

The owner of an office building is expanding the length and width of a parking lot by the same amount. The lot currently measures 120 ft by 80 ft, and the expansion will increase its area by 4,400 ft2. By how many feet should the length of the parking lot be increased? cap A is equal to l w

220 feet

20 feet

66 point 3 feet

1 point 2 feet

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Quadratics and Complex Numbers — Test Answers

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