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This module is from Elementary Algebra</link>by Denny Burzynski and Wade Ellis, Jr. Methods of solving quadratic equations as well as the logic underlying each method are discussed. Factoring, extraction of roots, completing the square, and the quadratic formula are carefully developed. The zero-factor property of real numbers is reintroduced. The chapter also includes graphs of quadratic equations based on the standard parabola, y = x^2, and applied problems from the areas of manufacturing, population, physics, geometry, mathematics (numbers and volumes), and astronomy, which are solved using the five-step method.This module contains the proficiency exam for the chapter "Quadratic Equations".

Proficiency exam

For the quadratic equations in the following problems, specify the values of a , b , and c .

( [link] ) 2 y 2 3 y + 10 = 0

a = 2 , b = 3 , c = 10

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( [link] ) 10 b 2 = 3 b

a = 10 , b = 3 , c = 0

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For the following problems, use the zero-factor property to solve each quadratic equation.

( [link] ) ( 3 x + 5 ) ( x 1 ) = 0

x = 5 3 , 1

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( [link] ) 3 b ( 2 b 1 ) = 0

b = 0 , 1 2

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( [link] ) ( a 8 ) 2 = 0

a = 8

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For the following problems, solve each quadratic equation by factoring.

( [link] ) 4 x 2 16 = 0

x = 2 , 2

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( [link] ) y 2 12 y + 32 = 0

y = 4 , 8

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( [link] ) a 2 5 a = 14

2 , 7

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( [link] ) 6 a 2 = 10 11 a

a = 5 2 , 2 3

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( [link] ) 2 x 2 = 2 5 x

x = 2 , 1 2

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( [link] ) x 3 25 x = 0

x = 0 , 5 , 5

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For the following problems, solve each quadratic equation by extraction of roots.

( [link] ) x 2 = 15

x = 15 , 15

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( [link] ) 3 a 2 18 = 0

a = 6 , 6

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( [link] ) ( x 5 ) 2 = 1

x = 4 , 6

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( [link] ) ( y + 11 ) 2 9 = 0

y = 8 , 14

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( [link] ) y 2 25 z 2 = 0 for y

y = 5 z , 5 z

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( [link] ) 6 a 2 18 b 2 c 2 for a

a = ± b c 3

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For the following problems, solve each quadratic equation using quadratic formula.

( [link] ) x 2 6 x 16 = 0

x = 2 , 8

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( [link] ) y 2 2 y 7 = 0

y = 1 ± 2 2

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( [link] ) ( m + 2 ) 2 5 = 0

m = 2 ± 5

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( [link] ) ( x + b ) 2 = c 2

x = b ± c

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( [link] ) ( x + 1 ) ( x + 4 ) = 6

x = 5 ± 33 2

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( [link] ) 5 z 2 5 z 5 = 2 z 2 z

z = 2 ± 19 3

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( [link] ) 2 m 2 = 5 m

m = 0 , 5 2

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For the following problems, solve each quadratic equation by completing the square.

( [link] ) x 2 + 6 x 8 = 0

x = 3 ± 17

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( [link] ) 2 x 2 + 7 x 12 = 0

x = 7 ± 145 4

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( [link] ) The product of two consecutive odd integers is 143. What are they?

11 and 13 or 11 and 13

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( [link] ) A study of the air quality by an environmental group suggests that t years from now the level of carbon monoxide in the air, in parts per million, will be given by the quadratic equation

A = 0.4 t 2 + 0.1 t + 3.1

where A represents the amount of carbon monoxide in the air.
(a) What is the level, in parts per million, of carbon monoxide in the air now?
(b) How many years from now will the level of carbon monoxide be at18.1 parts per million?

(a) 3.1   (b) 6 years from now

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( [link] ) The length of a rectangle is 6 inches longer than the width of the rectangle. Find the dimensions of the rectangle if the area is 112 square feet.

width = 1 + 1793 4 ; length = 1 + 1793 4

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For the following problems, construct the graphs of the following equations.

For the following problems, write the equation that corresponds to each graph.

( [link] )

A graph of a quadratic equation passing through three points with coordinates one, two; two, one; and three, two.

y = ( x 2 ) 2 + 1 or y = x 2 4 x + 5

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( [link] )

A graph of a quadratic equation passing through three points with coordinates negative four, negative three;negative three, negative two; and negative two, negtaive three.

y = ( x + 3 ) 2 2 or y = x 2 6 x 11

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Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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