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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

Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
Widad Reply
can you send the book attached ?
Ariel
?
Ariel
What is economics
Widad Reply
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn Reply
U(x,y) = (x×y)1/2 find mu of x for y
Desalegn
what is ecnomics
Jan Reply
this is the study of how the society manages it's scarce resources
Belonwu
what is macroeconomic
John Reply
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
etc
husaini
difference between firm and industry
husaini Reply
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from Qd  120 3P to Qd  90  3P and the supply function has shifted from QS  20  2P to QS 10  2P . a) Find the effect of this change on price and quantity. b) Which of the changes in demand and supply is higher?
Toofiq Reply
explain standard reason why economic is a science
innocent Reply
factors influencing supply
Petrus Reply
what is economic.
Milan Reply
scares means__________________ends resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Zarshad Reply
Why qualify 28 supplies
Milan
what are explicit costs
Nomsa Reply
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
David Reply
economic overview notes
Amahle Reply
identify a demand and a supply curve
Salome Reply
i don't know
Parul
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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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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