Deck 7: Quadratic Equations, Functions and Inequalities

Question 1

Solve the equation by using the square root property.

Answer 1

B

Question 2

Write the word or phrase that best completes each statement or answers the question.
Solve the quadratic equation by completing the square and applying the square root property.

Answer 2

Question 3

Write the word or phrase that best completes each statement or answers the question.
Solve the equation by using the square root property.

Answer 3

Question 4

Solve the equation by using the square root property.

Question 5

Question 6

Write the word or phrase that best completes each statement or answers the question.
Solve the equation by using the square root property.

Question 7

Solve the equation by using the square root property.

A) {7}
B) {±7}
C) {7i}
D) {±7i}

Question 8

Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial.

Question 9

Solve the quadratic equation by completing the square and applying the square root property.

Question 10

Solve the quadratic equation by completing the square and applying the square root property.

Question 11

Write the word or phrase that best completes each statement or answers the question.
Solve the quadratic equation by completing the square and applying the square root property.

Question 12

Solve the quadratic equation by completing the square and applying the square root property.

Question 13

Solve the quadratic equation by completing the square and applying the square root property.

Question 14

Solve the equation by using the square root property.

Question 15

Write the word or phrase that best completes each statement or answers the question.
Solve the equation by using the square root property.

Question 16

Solve the quadratic equation by completing the square and applying the square root property.

A) {-8i, 5i}
B) {-8, 5}
C) {-5, 8}
D) {-5i, 8i}

Question 17

Write the word or phrase that best completes each statement or answers the question.
Find the value of n so that the expression is a perfect square trinomial and then factor the trinomial.

Question 18

Solve the equation by using the square root property.

Question 19

Solve the equation by using the square root property.

Question 20

Find the value of k so that the expression is a perfect square trinomial and then factor the trinomial.

Question 21

Write the word or phrase that best completes each statement or answers the question.
A cable car carries tourists from street level down into a canyon, as shown in the figure below. The
horizontal distance d between the two cable support towers is 450 feet, and the length of the cable
between the towers is 3 times the vertical descent h (see figure). Find the vertical descent h into the
canyon. Round to the nearest tenth of a foot.

Question 22

If we ignore air resistance, the distance d(t) (in feet) that an object travels in free fall can be approximated by , where t is the time in seconds after the object was dropped. If a
Building is 1323 ft high, how long will it take an object to fall from the top of the building? Round
To one decimal place.

A) 9.1 sec
B) 2.3 sec
C) 36.4 sec
D) 12.9 sec

Question 23

Solve the equation by using the quadratic formula.

Question 24

Write the word or phrase that best completes each statement or answers the question.
The daily profit made by an automobile manufacturer is where x is the number of cars produced per shift. How many cars must be produced per shift for the
company to make a daily profit of $6000? Round any decimal part up to the next whole car.

Question 25

Write the word or phrase that best completes each statement or answers the question.
Solve the equation by using the quadratic formula.

Question 26

Write the word or phrase that best completes each statement or answers the question.

Question 27

a. Factor the expression b. Use the zero product rule and the quadratic formula to solve the equation = 0. There should be three solutions.

Question 28

The city of Morgana is 20 miles due west of Vining. Beckett is due north of Morgana. If the distance from Beckett to Vining is 2 miles less than 3 times the distance from Beckett to Morgana,
How far apart are Beckett and Morgana? Round to 1 decimal place.

A) 7.8 miles
B) 6.9 miles
C) 5.3 miles
D) 11.2 miles

Question 29

Solve the equation by using the quadratic formula.

Question 30

The daily profit made by an automobile manufacturer is where x is the number of cars produced per shift. How many cars must be produced per shift for the company to break even?

A) 10 or 40
B) 50
C) 25 or 30
D) None

Question 31

The hypotenuse of a right triangle is 7 ft long. One leg is 1.4 ft longer than the other leg. Find the lengths of the legs. Round to 1 decimal place.

A) 1.4 ft2 and 5.6 ft2
B) 1.4 ft and 5.6 ft
C) 4.1 ft2 and 5.7 ft2
D) 4.2 ft and 5.6 ft

Question 32

Solve the equation by using the quadratic formula.

Question 33

Solve the equation by using the quadratic formula.

Question 34

Solve the equation by using the quadratic formula.

A) {-0.06, -0.04}
B) {-6, -4}
C) {0.06i, 0.04i}
D) {4i, 6i}

Question 35

Write the word or phrase that best completes each statement or answers the question.
a. Factor the expression b. Use the zero product rule and the quadratic formula to solve the equation There should be three solutions.

Question 36

Solve for u.

Question 37

Solve the equation by using the quadratic formula.

A) {-1}
B) {-1, 7}
C) {1}
D) {1, -7}

Question 38

A square has an area of 87 square inches. What are the lengths of the sides? (Round to one decimal place if necessary.)

A) 9.3 in.
B) 348 in.
C) 21.8 in.
D) 7569 in.

Question 39

Write the word or phrase that best completes each statement or answers the question.
A 10 foot ladder is leaning against a vertical wall so that the distance from its base to the wall is 1
foot less than the distance from its top to the floor. How far away from the wall is the base of the
ladder? Round to the nearest hundredth of a foot.

Question 40

Question 41

Solve the quadratic equation by using any method.

Question 42

Use the discriminant to determine the type and number of solutions. x(2x + 11) = 40

A) Two imaginary solutions
B) Two rational solutions
C) Two irrational solutions
D) One rational solution

Question 43

A catapult is designed to launch circus performers from a raised platform. After launch, the height of the performer in feet is given by where t is seconds after launch. After how many seconds is the performer exactly 100 feet above the
Ground? Round to the nearest tenth of a second.

A) 5 seconds
B) 1.1 and 3.9 seconds
C) -0.4 and 5.4 seconds
D) 0.5 and 2.8 seconds

Question 44

Determine the discriminant. Then use it to determine the number of x-intercepts that the function has.

A) Discriminant: -44; no x-intercepts
B) Discriminant: -44; two x-intercepts
C) Discriminant: -172; no x-intercepts
D) Discriminant: -172; two x-intercepts

Question 45

Write the word or phrase that best completes each statement or answers the question.
Find the x- and y-intercepts of the function.

Question 46

Find the x- and y-intercepts of the function.

A) x-intercepts: ( 10, 0) and (- 10, 0); y-intercept: (0, -40)
B) x-intercept: ( 10, 0); y-intercept: none
C) x-intercepts: (0, 10) and (0, - 10); y-intercept: (-40, 0)
D) x-intercept: (0, 10); y-intercept: (-40, 0)

Question 47

Use the discriminant to determine the type and number of solutions:

A) Two rational solutions
B) One rational solution
C) Two irrational solutions
D) Two imaginary solutions

Question 48

Write the word or phrase that best completes each statement or answers the question.
A catapult is designed to launch circus performers from a raised platform. After launch, the height of the
performer in feet is given by where t is seconds after launch. After how many seconds is the performer at ground level? Round
to the nearest tenth of a second.

Question 49

Solve the equation by using substitution.

A) {5, -5}
B) {8, 125}
C) {8, -125}
D) {4, 25}

Question 50

Use the discriminant to determine the type and number of solutions.

A) Two rational solutions
B) Two irrational solutions
C) One rational solution
D) Two imaginary solutions

Question 51

Solve the quadratic equation by using any method.

Question 52

Use the discriminant to determine the type and number of solutions.

A) Two imaginary solutions
B) Two irrational solutions
C) Two rational solutions
D) One rational solution

Question 53

Solve the equation by using substitution.

Question 54

Solve the equation by using the quadratic formula.

Question 55

Find the discriminant and use it to determine the number and type of solutions.

A) 60: Two imaginary solutions
B) -60: One rational solutions
C) 60: Two irrational solutions
D) -60: Two imaginary solutions

Question 56

Solve the equation by using substitution.

Question 57

Solve the quadratic equation by using any method.

Question 58

Find the x-intercepts of the function.

Question 59

Find the x- and y-intercepts of the function.

Question 60

Write the word or phrase that best completes each statement or answers the question.
Solve the equation by using substitution.

Question 61

Find the vertex of the function.

A) (-19, 16)
B) (16, 19)
C) (19, 16)
D) (16, -19)

Question 62

Solve the equation by using substitution.

Question 63

Write the word or phrase that best completes each statement or answers the question.
Graph the function.

Question 64

Solve the equation.

Question 65

Graph the function.

Question 66

Solve the equation by using substitution.

A) {4, 11}
B) {-4, -11}
C) {-12, -5}
D) {4, -3}

Question 67

Graph the function.

Question 68

Solve the equation.

Question 69

Graph the function.

Question 70

Write the word or phrase that best completes each statement or answers the question.
Graph the function.

Question 71

Write the word or phrase that best completes each statement or answers the question.
Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then
write the maximum or minimum value.

Question 72

Graph the function.

Question 73

Write the equation of the axis of symmetry of the parabola.

A) x = -6
B) x = 6
C) y = 5
D) x = 5

Question 74

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point.

A) (-12, -8); maximum
B) (-8, 12); maximum
C) (12, -8); minimum
D) (-12, -8); minimum

Question 75

Graph the function.

Question 76

Write the word or phrase that best completes each statement or answers the question.
Solve the equation by using substitution.

Question 77

Solve the equation.

Question 78

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point.

A) (3, 12); minimum
B) (-3, 12); maximum
C) (3, 12); maximum
D) (12, 3); minimum

Question 79

Graph the function.

Question 80

Write the coordinates of the vertex and determine if the vertex is a maximum point or a minimum point. Then
write the maximum or minimum value.