Deck 8: Quadratic Equations, Functions, and Inequalities

Question 1

Which of the following is an example of a quadratic equation?

A) $5 x - 6 = 0$
B) $2 x ^ { 2 } - 6 x - 6 = 0$
C) $9 x ^ { 3 } + 3 x ^ { 2 } - 5 x + 8 = 0$
D) $\left| x ^ { 2 } - 1 \right| = 0$

Answer 1

$2 x ^ { 2 } - 6 x - 6 = 0$

Question 2

Which of the following equations would be obtained when solving $4 x ^ { 2 } + 8 x + 8 = 0$ by completing the square?

A) $\left( x ^ { 2 } + 1 \right) ^ { 2 } = - 1$
B) $( x + 1 ) ^ { 2 } = 3$
C) $( x + 1 ) ^ { 2 } = - 3$
D) $( x + 1 ) ^ { 2 } = - 1$

Answer 2

$( x + 1 ) ^ { 2 } = - 1$

Question 3

Solve $( x + 5 ) ^ { 2 } = 80$ by square root property.

A) $\{ - 9 \sqrt { 5 } , - \sqrt { 5 } \}$
B) $\{ - 5 + 4 \sqrt { 5 } \}$
C) $\{ 5 \pm 4 \sqrt { 5 } \}$
D) $\{ - 5 \pm 4 \sqrt { 5 } \}$

Answer 3

$\{ - 5 \pm 4 \sqrt { 5 } \}$

Question 4

Use the square root property to solve the equation.

Answer 4

Question 5

Solve $( x + 1 ) ^ { 2 } - 7 = 0$ by square root property.

A) $\{ - 1 \pm 4 \sqrt { 5 } \}$
B) $\{ 1 \pm 4 \sqrt { 5 } \}$
C) $\{ 1 \pm \sqrt { 7 } \}$
D) $\{ - 1 \pm \sqrt { 7 } \}$

Question 6

The __________ coefficient of is 1, and the constant term is 36.

Question 7

Solve $2 x ^ { 2 } - 9 = 0$ by the square root property.

A) $\left\{ \frac { 9 } { 2 } \right\}$
B) $\{ \pm 3 \}$
C) $\left\{ \pm \frac { 3 \sqrt { 2 } } { 2 } \right\}$
D) $\{ - 3 \}$

Question 8

What number is added to each side of the equation $4 x ^ { 2 } + 48 x = 7$ in completing the square?

A) 75
B) 36
C) 4
D) 48

Question 9

What is the next step in solving $4 x ^ { 2 } - 12 x = 9$ by completing the square?

A) Add -9 to each side of the equation.
B) Take one-half of -12 and add to each side of the equation.
C) Take one-half of 4 and square it and then add this number to each side of the equation.
D) Divide each side of the equation by 4 .

Question 10

Solve $( x - 7 ) ^ { 2 } = 96$ by the square root property.

A) $\{ - 11 \sqrt { 6 } , \sqrt { 6 } \}$
B) $\{ - \sqrt { 6 } , 11 \sqrt { 6 } \}$
C) $\{ - 7 \pm 4 \sqrt { 6 } \}$
D) $\{ 7 \pm 4 \sqrt { 6 } \}$

Question 11

Use the square root property to solve the equation.

Question 12

When we add 9 to , we say that we have completed the _________.

Question 13

Use the square root property to solve the equation.

Question 14

Solve $x ^ { 2 } + 28 = 0$ by the square root property.

A) $\{ \pm 7 i \sqrt { 2 } \}$
B) $\{ \pm 2 i \sqrt { 7 } \}$
C) $\{ \pm 7 \sqrt { 2 } \}$
D) $\{ \pm 2 \sqrt { 7 } \}$

Question 15

Solve by square root property: $2 x ^ { 2 } = 144$

A) $\{ 6 \pm \sqrt { 2 } \}$
B) $\{ \pm 2 \}$
C) $\{ \pm 2 \sqrt { 6 } \}$
D) $\{ \pm 6 \sqrt { 2 } \}$

Question 16

is called a(n) __________ square trinomial because it factors as .

Question 17

To complete the square on , add the square of ________ of the coefficient of x .

Question 18

Solve $x ^ { 2 } - 10 x - 4 = 0$ by completing the square.

A) $\{ 5 \pm \sqrt { 89 } \}$
B) $\{ - 5 \pm \sqrt { 89 } \}$
C) $\{ 5 \pm \sqrt { 29 } \}$
D) $\{ - 5 \pm \sqrt { 29 } \}$

Question 19

An equation of the form , where , is called a __________ equation.

Question 20

Use the square root property to solve the equation.

Question 21

Use the square root property to solve the equation.

Question 22

Use the square root property to solve the equation.

Question 23

Use the square root property to solve the equation.

Question 24

Use the square root property to solve the equation.

Question 25

Use the square root property to solve the equation.

Question 26

The __________ coefficient of is 1, and the __________ term is 36.

Question 27

Solve the equation.

Question 28

Use the square root property to solve the equation.

Question 29

Use the square root property to solve the equation.

Question 30

Use the square root property to solve the equation.

Question 31

Use completing the square to solve the equation.

Question 32

Use completing the square to solve the equation.

Question 33

Solve the equation.

Question 34

Use the square root property to solve the equation.

Question 35

Solve by completing the square.

Question 36

Use completing the square to solve the equation.

Question 37

Use the square root property to solve the equation.

Question 38

Use completing the square to solve the equation.

Question 39

Solve $6 x ^ { 2 } + 12 x + 5 = 0$ by the quadratic formula.

A) $\left\{ \frac { - 6 \pm \sqrt { 6 } } { 6 } \right\}$
B) $\{ - 1 \pm \sqrt { 6 } \}$
C) $\left\{ \frac { 6 \pm \sqrt { 6 } } { 6 } \right\}$
D) $\{ \pm \sqrt { 6 } \}$

Question 40

Solve the equation.

Question 41

Tickets to a dance cost $5.00 and the projected attendance is 350 people. It is further projected that for every $0.50 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $3,360?

A) $9.50
B) $11.00
C) $19.00
D) $12.00

Question 42

Solve the equation.

Question 43

Solve: $\frac { x ^ { 2 } } { 3 } - \frac { x } { 2 } = \frac { 3 } { 8 }$

A) $\left\{ \frac { 3 } { 2 } \right\}$
B) $\left\{ \frac { 3 } { 4 } \pm \frac { 3 \sqrt { 3 } } { 4 } i \right\}$
C) none of these
D) $\left\{ \frac { 3 \pm 3 \sqrt { 3 } } { 4 } \right\}$

Question 44

Solve by quadratic formula: $3 x ^ { 2 } - 4 x + 3 = 0$

A) $\left\{ - \frac { 2 } { 3 } \pm \frac { \sqrt { 5 } } { 3 } \right\}$
B) none of these
C) $\left\{ \frac { 2 } { 3 } \pm \frac { \sqrt { 5 } } { 3 } i \right\}$
D) $\left\{ \frac { 2 } { 3 } \pm \frac { 2 \sqrt { 5 } } { 3 } i \right\}$

Question 45

Solve the equation.

Question 46

Use completing the square to solve the equation.

Question 47

Use the square root property to solve the equation.

Question 48

Let . For what value(s) of x is ?

Question 49

Solve the equation.

Question 50

Use completing the square to solve the equation.

Question 51

Solve by the quadratic formula: $x ^ { 2 } = 4 x - 2$

A) $\{ 2 \pm \sqrt { 2 } \}$
B) $\{ 2 \pm 2 \sqrt { 2 } \}$
C) $\{ 2 \pm i \sqrt { 2 } \}$
D) $\{ 2 \pm 2 i \sqrt { 2 } \}$

Question 52

Solve the equation.

Question 53

Solve $\frac { x ^ { 2 } } { 4 } + \frac { x } { 5 } = \frac { 1 } { 20 }$ by any method.

A) $\left\{ - \frac { 1 } { 5 } , 1 \right\}$
B) $\left\{ - 1 , \frac { 1 } { 5 } \right\}$
C) $\left\{ - \frac { 1 } { 5 } \pm \frac { i \sqrt { 3 } } { 5 } \right\}$
D) $\left\{\frac{1}{5} \pm \frac{i \sqrt{3}}{5}\right.\}$

Question 54

Use the square root property to solve the equation.

Question 55

Use completing the square to solve the equation.

Question 56

The solutions of $a x ^ { 2 } + b x + c = 0$ $( a \neq 0 )$ are

A) $x = - b \pm \frac { \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$
B) $x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$
C) $x = \frac { \pm b \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$
D) $x = \frac { b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a }$

Question 57

Solve the equation.

Question 58

Use completing the square to solve the equation.

Question 59

What number must be added to to make a perfect-square trinomial?

Question 60

Solve $3 x ^ { 2 } - 4 x = - 2$ by the quadratic formula.

A) $\left\{ \frac { 2 \pm \sqrt { 3 } } { 3 } \right\}$
B) $\left\{ - \frac { 2 } { 3 } \pm \frac { i \sqrt { 2 } } { 3 } \right\}$
C) $\left\{ \frac { 2 } { 3 } \pm \frac { i \sqrt { 2 } } { 3 } \right\}$
D) $\left\{ \frac { 2 \pm \sqrt { 2 } } { 3 } \right\}$

Question 61

A box with no top is to be made by cutting a 2-inch square from each corner of the square sheet of metal. After bending up the sides, the volume of the box is to be 512 cubic inches. What are the dimensions of the square sheet?

A) 17 inches by 17 inches
B) 6 inches by 6 inches
C) 19 inches by 19 inches
D) 20 inches by 20 inches

Question 62

The _________ form of a quadratic equation is .

Question 63

is called the __________ formula.

Question 64

Suppose a rectangular movie screen has an area of 11,136 square feet. Find the dimensions of the screen if it is 20 feet longer than it is wide. __________ ft by __________ ft

Question 65

Solve the equation.

Question 66

Solve the equation. Approximate the solutions to two decimal places.

Question 67

Solve the equation. Approximate the solutions to two decimal places.

Question 68

Use the quadratic formula to solve the equation.

Question 69

Evaluate the expression.

Question 70

The hypotenuse of a right triangle is 6.1 units long. The longer leg is 4.9 units longer than the shorter leg. Find the lengths of the sides of the triangle. longer leg __________ units shorter leg __________ units

Question 71

The formula is called the quadratic formula.

Question 72

Use the quadratic formula to solve the equation.

Question 73

Write the equation in standard form.

Question 74

Solve the equation.

Question 75

Evaluate the expression.

Question 76

Simplify the following.

Question 77

Solve the equation.

Question 78

For the following quadratic equation, find , and . __________ __________ __________

Question 79

Tickets to a school dance cost $4, and the projected attendance is 300 persons. It is further projected that for every $0.1 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the receipts from the dance be $1,242?

Question 80

For the following quadratic equation, find , and .