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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket 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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