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Algebra A Combined Function

Elayn Martin-Gay

Chapter 11

Quadratic Equations and Functions - all with Video Answers

Educators

Section 1

Solving Quadratic Equations by Completing the Square

00:34

Problem 1

Use the square root property to solve each equation.
$$
x^{2}=16
$$

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00:29

Problem 2

Use the square root property to solve each equation.
$$
x^{2}=49
$$

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00:34

Problem 3

Use the square root property to solve each equation.
$$
x^{2}-7=0
$$

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00:32

Problem 4

Use the square root property to solve each equation.
$$
x^{2}-11=0
$$

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00:38

Problem 5

Use the square root property to solve each equation.
$$
x^{2}=18
$$

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00:36

Problem 6

Use the square root property to solve each equation.
$$
y^{2}=20
$$

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00:32

Problem 7

Use the square root property to solve each equation.
$$
3 z^{2}-30=0
$$

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00:28

Problem 8

Use the square root property to solve each equation.
$$
2 x^{2}=4
$$

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00:39

Problem 9

Use the square root property to solve each equation.
$$
(x+5)^{2}=9
$$

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00:37

Problem 10

Use the square root property to solve each equation.
$$
(y-3)^{2}=4
$$

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00:41

Problem 11

Use the square root property to solve each equation.
$$
(z-6)^{2}=18
$$

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00:44

Problem 12

Use the square root property to solve each equation.
$$
(y+4)^{2}=27
$$

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00:57

Problem 13

Use the square root property to solve each equation.
$$
(2 x-3)^{2}=8
$$

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00:59

Problem 14

Use the square root property to solve each equation.
$$
(4 x+9)^{2}=6
$$

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00:43

Problem 15

Use the square root property to solve each equation.
$$
x^{2}+9=0
$$

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00:34

Problem 16

Use the square root property to solve each equation.
$$
x^{2}+4=0
$$

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00:49

Problem 17

Use the square root property to solve each equation.
$$
x^{2}-6=0
$$

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00:28

Problem 18

Use the square root property to solve each equation.
$$
y^{2}-10=0
$$

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00:45

Problem 19

Use the square root property to solve each equation.
$$
2 z^{2}+16=0
$$

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00:41

Problem 20

Use the square root property to solve each equation.
$$
3 p^{2}+36=0
$$

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00:45

Problem 21

Use the square root property to solve each equation.
$$
(3 x-1)^{2}=-16
$$

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00:49

Problem 22

Use the square root property to solve each equation.
$$
(4 y+2)^{2}=-25
$$

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00:34

Problem 23

Use the square root property to solve each equation.
$$
(z+7)^{2}=5
$$

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00:31

Problem 24

Use the square root property to solve each equation.
$$
(x+10)^{2}=11
$$

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00:45

Problem 25

Use the square root property to solve each equation.
$$
(x+3)^{2}+8=0
$$

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00:43

Problem 26

Use the square root property to solve each equation.
$$
(y-4)^{2}+18=0
$$

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00:29

Problem 27

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial. See Examples 5 and 6.
$$
x^{2}+16 x
$$

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Problem 28

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
y^{2}+2 y
$$

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00:36

Problem 29

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
z^{2}-12 z
$$

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00:29

Problem 30

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
x^{2}-8 x
$$

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Problem 31

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
p^{2}+9 p
$$

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Problem 32

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
n^{2}+5 n
$$

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00:33

Problem 33

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
r^{2}-r
$$

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00:44

Problem 34

Add the proper constant to each binomial so that the resulting trinomial is a perfect square trinomial. Then factor the trinomial.
$$
p^{2}-7 p
$$

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00:38

Problem 35

Solve each equation by completing the square. See Examples 7 through 9
$$
x^{2}+8 x=-15
$$

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00:36

Problem 36

Solve each equation by completing the square.
$$
y^{2}+6 y=-8
$$

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00:42

Problem 37

Solve each equation by completing the square.
$$
x^{2}+6 x+2=0
$$

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Problem 38

Solve each equation by completing the square.
$$
x^{2}-2 x-2=0
$$

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Problem 39

Solve each equation by completing the square.
$$
x^{2}+x-1=0
$$

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Problem 40

Solve each equation by completing the square.
$$
x^{2}+3 x-2=0
$$

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Problem 41

Solve each equation by completing the square.
$$
x^{2}+2 x-5=0
$$

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00:27

Problem 42

Solve each equation by completing the square.
$$
x^{2}-6 x+3=0
$$

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00:48

Problem 43

Solve each equation by completing the square.
$$
y^{2}+y-7=0
$$

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00:51

Problem 44

Solve each equation by completing the square.
$$
x^{2}-7 x-1=0
$$

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00:31

Problem 45

Solve each equation by completing the square.
$$
x^{2}+8 x+1=0
$$

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00:35

Problem 46

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

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00:59

Problem 47

Solve each equation by completing the square.
$$
3 p^{2}-12 p+2=0
$$

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01:49

Problem 48

Solve each equation by completing the square.
$$
2 x^{2}+14 x-1=0
$$

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01:33

Problem 49

Solve each equation by completing the square.
$$
2 x^{2}+7 x=4
$$

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01:16

Problem 50

Solve each equation by completing the square.
$$
3 x^{2}-4 x=4
$$

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01:26

Problem 51

Solve each equation by completing the square.
$$
3 y^{2}+6 y-4=0
$$

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01:03

Problem 52

Solve each equation by completing the square.
$$
2 y^{2}+12 y+3=0
$$

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00:46

Problem 53

Solve each equation by completing the square.
$$
y^{2}+2 y+2=0
$$

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00:48

Problem 54

Solve each equation by completing the square.
$$
x^{2}+4 x+6=0
$$

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00:59

Problem 55

Solve each equation by completing the square.
$$
2 a^{2}+8 a=-12
$$

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01:01

Problem 56

Solve each equation by completing the square.
$$
3 x^{2}+12 x=-14
$$

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Problem 57

Solve each equation by completing the square.
$$
2 x^{2}-x+6=0
$$

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01:41

Problem 58

Solve each equation by completing the square.
$$
4 x^{2}-2 x+5=0
$$

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00:45

Problem 59

Solve each equation by completing the square.
$$
x^{2}+10 x+28=0
$$

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00:53

Problem 60

Solve each equation by completing the square.
$$
y^{2}+8 y+18=0
$$

Victor Salazar
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01:11

Problem 61

Solve each equation by completing the square.
$$
z^{2}+3 z-4=0
$$

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01:01

Problem 62

Solve each equation by completing the square.
$$
y^{2}+y-2=0
$$

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Problem 63

Solve each equation by completing the square.
$$
2 x^{2}-4 x+3=0
$$

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00:57

Problem 64

Solve each equation by completing the square.
$$
9 x^{2}-36 x=-40
$$

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01:33

Problem 65

Solve each equation by completing the square.
$$
3 x^{2}+3 x=5
$$

Victor Salazar
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01:17

Problem 66

Solve each equation by completing the square.
$$
5 y^{2}-15 y=1
$$

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01:25

Problem 67

Use the formula to solve Exercises 67 through 70.
Find the rate $r$ at which $\$ 3000$ grows to $\$ 4320$ in 2 years.

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00:54

Problem 68

Use the formula to solve.
Find the rate $r$ at which $\$ 800$ grows to $\$ 882$ in 2 years.

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00:39

Problem 69

Use the formula to solve.
Find the rate $r$ at which $\$ 810$ grows to approximately $\$ 1000$ in 2 years.

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00:37

Problem 70

Use the formula to solve.
Find the rate $r$ at which $\$ 2000$ grows to $\$ 2880$ in 2 years.

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00:58

Problem 71

Neglecting air resistance, the distance $s(t)$ in feet traveled by a freely falling object is given by the function $s(t)=16 t^{2}$, where t is time in seconds. Use this formula to solve Exercises 71 through $74 .$ Round answers to two decimal places.
The Petronas Towers in Kuala Lumpur, completed in 1998, are the tallest buildings in Malaysia. Each tower is 1483 feet tall. How long would it take an object to fall to the ground from the top of one of the towers? (Source: Council on Tall Buildings and Urban Habitat, Lehigh University)

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00:43

Problem 72

Neglecting air resistance, the distance $s(t)$ in feet traveled by a freely falling object is given by the function $s(t)=16 t^{2}$, where t is time in seconds. Use this formula to solve. Round answers to two decimal places.
The Burj Khalifa, the tallest building in the world, was completed in 2009 in Dubai. It is estimated to be 2717 feet tall. How long would it take an object to fall to the ground from the top of the building? (Source: Council on Tall Buildings and Urban Habitat)

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00:31

Problem 73

Neglecting air resistance, the distance $s(t)$ in feet traveled by a freely falling object is given by the function $s(t)=16 t^{2}$, where t is time in seconds. Use this formula to solve. Round answers to two decimal places.
The Rogun Dam in Tajikistan (part of the former USSR that borders Afghanistan) is the tallest dam in the world at 1100 feet. How long would it take an object to fall from the top to the base of the dam? (Source: U.S. Committee on Large Dams of the International Commission on Large Dams)

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00:35

Problem 74

Neglecting air resistance, the distance $s(t)$ in feet traveled by a freely falling object is given by the function $s(t)=16 t^{2}$, where t is time in seconds. Use this formula to solve. Round answers to two decimal places.
The Hoover Dam, located on the Colorado River on the border of Nevada and Arizona near Las Vegas, is 725 feet tall. How long would it take an object to fall from the top to the base of the dam? (Source: U.S. Committee on Large Dams of the International Commission on Large Dams)

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Problem 75

Solve. The area of a square room is 225 square feet. Find the dimensions of the room.

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Problem 76

Solve.The area of a circle is $36 \pi$ square inches. Find the radius of the circle.

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01:07

Problem 77

Solve.An isosceles right triangle has legs of equal length. If the hypotenuse is 20 centimeters long, find the length of each leg.

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Problem 78

Solve.The top of a square coffee table has a diagonal that measures 30 inches. Find the length of each side of the top of the coffee table.

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00:36

Problem 79

Simplify each expression. See Section 10.1.
$$
\frac{6+4 \sqrt{5}}{2}
$$

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00:28

Problem 80

Simplify each expression.
$$
\frac{10-20 \sqrt{3}}{2}
$$

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00:35

Problem 81

Simplify each expression.
$$
\frac{3-9 \sqrt{2}}{6}
$$

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00:45

Problem 82

Simplify each expression.
$$
\frac{12-8 \sqrt{7}}{16}
$$

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Problem 83

Evaluate $\sqrt{b^{2}-4 a c}$ for each set of values. See Section $10.3 .$
$$
a=2, b=4, c=-1
$$

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00:46

Problem 84

Evaluate $\sqrt{b^{2}-4 a c}$ for each set of values.
$$
a=1, b=6, c=2
$$

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00:50

Problem 85

Evaluate $\sqrt{b^{2}-4 a c}$ for each set of values.
$$
a=3, b=-1, c=-2
$$

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00:46

Problem 86

Evaluate $\sqrt{b^{2}-4 a c}$ for each set of values.
$$
a=1, b=-3, c=-1
$$

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00:48

Problem 87

For Exercises $87-92$, without solving, determine whether the solutions of each equation are real numbers or complex, but not real numbers. See the Concept Check in this section.
$$
(x+1)^{2}=-1
$$

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Problem 88

Without solving, determine whether the solutions of each equation are real numbers or complex, but not real numbers. See the Concept Check in this section.
$$
(y-5)^{2}=-9
$$

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Problem 89

Without solving, determine whether the solutions of each equation are real numbers or complex, but not real numbers. See the Concept Check in this section.
$$
3 z^{2}=10
$$

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Problem 90

Without solving, determine whether the solutions of each equation are real numbers or complex, but not real numbers. See the Concept Check in this section.
$$
4 x^{2}=17
$$

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Problem 91

Without solving, determine whether the solutions of each equation are real numbers or complex, but not real numbers. See the Concept Check in this section.
$$
(2 y-5)^{2}+7=3
$$

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Problem 92

Without solving, determine whether the solutions of each equation are real numbers or complex, but not real numbers. See the Concept Check in this section.
$$
(3 m+2)^{2}+4=1
$$

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Problem 93

In your own words, explain how to calculate the number that will complete the square on an expression such as $x^{2}-5 x$.

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Problem 94

In your own words, what is the difference between simple interest and compound interest?

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Problem 95

If you are depositing money in an account that pays $4 \%,$ would you prefer the interest to be simple or compound? Explain your answer.

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Problem 96

If you are borrowing money at a rate of $10 \%,$ would you prefer the interest to be simple or compound? Explain your answer.

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01:04

Problem 97

Find two possible missing terms so that each is a perfect square trinomial.
$$
x^{2}+1+16
$$

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Problem 98

Find two possible missing terms so that each is a perfect square trinomial.
$$
y^{2}+\quad+9
$$

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01:10

Problem 99

$A$ common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity and the quantity demanded. For Exercises 99 and 100, $p$ represents the unit price and $x$ represents the quantity demanded in thousands.
A manufacturing company has found that the demand equation for a certain type of scissors is given by the equation $p=-x^{2}+47$. Find the demand for the scissors if the price is $\$ 11$ per pair.

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00:45

Problem 100

$A$ common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity and the quantity demanded,$p$ represents the unit price and $x$ represents the quantity demanded in thousands.
Acme, Inc., sells desk lamps and has found that the demand equation for a certain style of desk lamp is given by the equation $p=-x^{2}+15 .$ Find the demand for the desk lamp if the price is $\$ 7$ per lamp.

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