Deck 8: Quadratic Equations and Functions; Inequalities; and Algebra, Composition, and Inverses of Functions

Question 1

Use the factoring method to solve the equation.

A) ,
B) ,
C) ,
D) ,
E) ,

Answer 1

,

Question 2

Use the method of completing the square to solve the quadratic equation.

A)
B)
C)
D)
E)

Answer 2

Question 3

Use the quadratic formula to find all real solutions of the equation.

A)
B)
C)
D)
E) no real solutions

Answer 3

Question 4

The area of a rectangular region is 187 square feet. If the length and width are each increased by 5 feet, the area is increased by 165 square feet. Find the length and width of the original rectangle.

A) 13 feet by 19 feet
B) 11 feet by 17 feet
C) 10 feet by 16 feet
D) 8 feet by 14 feet
E) 12 feet by 18 feet

Question 5

Solve a formula for the indicated variable. , for .

A)
B)
C)
D)

Question 6

The area of a circle is numerically equal to 8 times the circumference of the circle. Find the length of a radius of the circle.

A) 16
B) 17
C) 16
D) 15
E) 8

Question 7

The height in feet of a rocket in flight is given by the formula , where is the time of the flight in seconds. How long will it take for the rocket to hit the ground?

A) 11 sec
B) 10 sec
C) 8 sec
D) 12 sec
E) 13 sec

Question 8

Factor the trinomial square and use the square root method to solve the equation.

A) ,
B) ,
C) ,
D) ,

Question 9

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) rational, equal
D) irrational, unequal

Question 10

The area of a tennis court is 2,128 square feet (see illustration). The length of the court is times the width. Find the length and width of the tennis court.

A) 94 feet by 25 feet
B) 82 feet by 26 feet
C) 85 feet by 25 feet
D) 76 feet by 22 feet
E) 76 feet by 28 feet

Question 11

Factor the trinomial square and use the square root method to solve the equation.

A)
B)
C)
D)
E)

Question 12

Solve a formula for the indicated variable. , for .

A)
B)
C)
D)

Question 13

Solve the equation by completing the square.

A) ,
B) ,
C) ,
D) ,
E) ,

Question 14

Solve the equation.

A)
B)
C)
D)
E)

Question 15

Solve a formula for the indicated variable. , for .

A)
B)
C)
D)

Question 16

When a wholesaler sells CD players, the revenue is . How many CD players would the wholesaler have to sell to receive ?

A) CD players
B) CD players
C) CD players
D) CD players
E) CD players

Question 17

Use the quadratic formula to find all real solutions of the equation.

A) x = 10, x = 4
B) x = 5, x = -2
C) x = 5, x = 4
D) x = -5, x = 2
E) x = 5, x = 2

Question 18

Use the method of completing the square to solve the quadratic equation.

A)
B)
C)
D)
E)

Question 19

Use the square root method to solve the equation.

A)
B)
C)
D)
E)

Question 20

The distance (in feet) that an object will fall in seconds is given by the formula . How long will it take an object to fall 784 feet?

A) 7 sec
B) 49 sec
C) 9 sec
D) 6 sec
E) 48 sec

Question 21

Graph the function.

A)
B)
C)
D)

Question 22

Which of the following graphs accurately represents the equation? f ( x ) = -( x - 2)² - 4

A)
B)
C)
D)

Question 23

Graph the function. f ( x ) = x ² + 3

A)
B)
C)
D)
E)

Question 24

Draw the graph using a translation of the graph of .

A)
B)
C)
D)
E)

Question 25

Solve the equation and verify that the sum of the solutions is - and the product of the solutions is .

A)
B)
C)
D)

Question 26

Solve the equation and verify that the sum of the solutions is - and the product of the solutions is .

A)
B)
C)
D)

Question 27

Graph the function. f ( x ) = 2 x ²

A)
B)
C)
D)

Question 28

Graph the function. f ( x ) = x ² - 2 x - 1

A)
B)
C)
D)

Question 29

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

A) rational, equal
B) irrational, unequal
C) irrational, equal
D) nonreal complex numbers, complex conjugates
E) rational, unequal

Question 30

Graph the function. f ( x ) = ( x - 2)²

A)
B)
C)
D)

Question 31

Graph the function.

A)
B)
C)
D)

Question 32

Use the quadratic formula to find all real solutions of the equation.

A)
B)
C)
D)
E) no real solutions

Question 33

Use the discriminant to determine what type of solutions exist for the quadratic equation. Do not solve the equation.

A) nonreal complex numbers, complex conjugates
B) rational, unequal
C) irrational, unequal
D) rational, equal
E) irrational, equal

Question 34

Graph the function. f ( x ) = -2(( x - 3)² - 1)

A)
B)
C)
D)

Question 35

Graph the function.

A)
B)
C)
D)

Question 36

Graph the function. f ( x ) = 2 x ² - 5

A)
B)
C)
D)

Question 37

Solve the equation and verify that the sum of the solutions is - and the product of the solutions is .

A)
B)
C)
D)

Question 38

For the following function, first sketch the graph of its associated function, . Then draw the graph using translation and/or a reflection.

A)
B)
C)
D)
E)

Question 39

Use the quadratic formula to find all real solutions of the equation.

A) x = 18, x = 8
B) x = 9, x = -4
C) x = 9, x = 8
D) x = -9, x = 4
E) x = 9, x = 4

Question 40

Graph the function.

A)
B)
C)
D)

Question 41

Find the coordinates of the vertex of the graph of the equation. If necessary, complete the square on x to write the equation in the form y = a ( x - h ) ² + k . Do not graph the equation.

A)
B)
C)
D)
E)

Question 42

Graph the inequality. y > x ² - 5

A)
B)
C)
D)

Question 43

Graph the inequality.

A)
B)
C)
D)
E)

Question 44

Find the vertex of the parabola and graph it.

A)
B)
C)
D)
E)

Question 45

Find the vertex of the parabola and graph it.

A)
B)
C)
D)
E)

Question 46

Find the coordinates of the vertex of the graph of the equation. If necessary, complete the square on x to write the equation in the form y = a ( x - h )² + k . Do not graph the equation. y = -4( x - 3)²

A) (0, -4)
B) (5, 0)
C) (-4, 0)
D) (0, 3)
E) (3, 0)

Question 47

An arch of the bridge shown in the following figure is semielliptical, and the major axis is horizontal. The arch is w = 40 feet wide and h = 15 feet high. Find the height of the arch d = 5 feet from the center of the base.

A)
B)
C)
D)
E)

Question 48

Solve the inequality.

A)
B)
C)
D)
E)

Question 49

For design purposes, the large gear in the illustration is the circle . The smaller gear is a circle centered at and tangent to the larger circle. Find the equation of the smaller gear.

A)
B)
C)
D)
E)

Question 50

Solve the inequality.

A)
B)
C)
D)
E) no solution

Question 51

Which of the following graphs accurately represents the equation shown below? f ( x ) = -3 x ² + 3 x + 1

A)
B)
C)
D)

Question 52

Find the vertex of the parabola and graph it.

A)
B)
C)
D)
E)

Question 53

Solve the inequality.

A)
B)
C)
D)
E) no solution

Question 54

Solve the inequality.

A)
B)
C)
D)

Question 55

Graph the function. f ( x ) = 2 x ² - 8 x +5

A)
B)
C)
D)

Question 56

Find the coordinates of the vertex of the graph of the equation. If necessary, complete the square on x to write the equation in the form y = a ( x - h ) ² + k . Do not graph the equation.

A)
B)
C)
D)
E)

Question 57

Solve the inequality.

A)
B)
C)
D)
E) no solution

Question 58

Solve the inequality.

A)
B)
C)
D)
E) no solution

Question 59

Graph the inequality.

A)
B)
C)
D)
E)

Question 60

The shapes of the suspension cables in certain types of bridges are parabolic. The suspension cable for the bridge shown in the illustration is described by y = 0.372 x ². Find y if x = -20.

A) 158.8
B) 258.8
C) 137.8
D) 128.8
E) 148.8

Question 61

The graph below represents a function. Use the horizontal line test to decide whether the function is one-to-one. Answer yes or no .

Question 62

The graph below represents a function. Use the horizontal line test to decide whether the function is one-to-one. Answer yes or no .

Question 63

Julia made a purchase at a furniture store, but it was too big and did not fit into her car. So, she arranged to have the store deliver the purchase for her. She paid for her purchase, plus the sales taxes, plus the fee. The taxes are 5 % and the fee is $25. Write a function t ( x ) for the total, after taxes, on the purchase amount x . Write another function f ( x ) for the total, including the delivery fee, on the purchase amount x . How much money did Julia spend, if she made a $440 purchase?

A) t ( x ) = 0.05 x ; f ( x ) = x + 25 ; $47
B) t ( x ) = 1.05 x ; f ( x ) = x + 25 ; $487.00
C) t ( x ) = 1.05 x ; f ( x ) = x + 25 ; $488.25
D) t ( x ) = 0.05 x ; f ( x ) = x + 25 ; $487.00

Question 64

If , find .

A) 6 a ² + 6 ah + 2 h ² - 2 a - h + 6
B) 2 a ² + 6 ah + h ² - 2 a + h
C) 4 a ² + 6 ah + 6 h ² - 2 a - h
D) 2 a ² + 2 ah + 2 h ² - 2 a - h + 6
E) 6 a ² - 6 ah + 2 h ² - 2 a - h + 6

Question 65

Determine whether the function is one-to-one.

A) no
B) yes

Question 66

Determine whether the function is one-to-one.

A) yes
B) no

Question 67

Mark works forty hours a week at a clothing store. His weekly salary is $220, plus he receives a 5% commission on sales over $1,000. Given the functions f ( x ) = 0.05 x and g ( x ) = x - 1,000, which of two compositions, ( f o g )( x ) or ( g o f )( x ), represents Mark's commission?

A) ( f o g )( x )
B) ( g o f )( x )

Question 68

Find for f ( x ) = - x ² - 8.

A) h + a
B) -8
C) -2 a - h
D) 8 a
E) -2 a ² - h

Question 69

Find the inverse of the given function and express it in the form . Verify the result by showing that .

A)
B)
C)
D)
E)

Question 70

Determine for the pair of functions and .

A)
B)
C)
D)
E)

Question 71

Find the inverse of the function and express it using notation.

A)
B)
C)
D)
E)

Question 72

If f ( x ) = -5 x - 7, find .

A) -7 h
B) -5
C) 5
D) -5 a
E) -7

Question 73

Determine for the pair of functions and .

A)
B)
C)
D)
E)

Question 74

The graph below represents a function. Use the horizontal line test to decide whether the function is one-to-one. Answer yes or no .

Question 75

Find the inverse of the given function and express it in the form . Verify the result by showing that .

A)
B)
C)
D)
E)

Question 76

Determine for the pair of functions and .

A)
B)
C)
D)
E)

Question 77

Determine whether the function is one-to-one.

A) yes
B) no

Question 78

A high pressure area promises increasingly warmer weather for the next 48 hours. The temperature is now 34° Celsius and is expected to rise 1° every 6 hours. Express the Fahrenheit temperature as a function of the number of hours t from now. ( Hint: )

A)
B)
C)
D)
E)