<< Chapter < Page Chapter >> Page >
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

Got questions? Get instant answers now!

( [link] ) 10 b 2 = 3 b

a = 10 , b = 3 , c = 0

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

b = 0 , 1 2

Got questions? Get instant answers now!

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

a = 8

Got questions? Get instant answers now!

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

( [link] ) 4 x 2 16 = 0

x = 2 , 2

Got questions? Get instant answers now!

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

y = 4 , 8

Got questions? Get instant answers now!

( [link] ) a 2 5 a = 14

2 , 7

Got questions? Get instant answers now!

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

a = 5 2 , 2 3

Got questions? Get instant answers now!

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

x = 2 , 1 2

Got questions? Get instant answers now!

( [link] ) x 3 25 x = 0

x = 0 , 5 , 5

Got questions? Get instant answers now!

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

( [link] ) x 2 = 15

x = 15 , 15

Got questions? Get instant answers now!

( [link] ) 3 a 2 18 = 0

a = 6 , 6

Got questions? Get instant answers now!

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

x = 4 , 6

Got questions? Get instant answers now!

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

y = 8 , 14

Got questions? Get instant answers now!

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

y = 5 z , 5 z

Got questions? Get instant answers now!

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

a = ± b c 3

Got questions? Get instant answers now!

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

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

x = 2 , 8

Got questions? Get instant answers now!

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

y = 1 ± 2 2

Got questions? Get instant answers now!

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

m = 2 ± 5

Got questions? Get instant answers now!

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

x = b ± c

Got questions? Get instant answers now!

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

x = 5 ± 33 2

Got questions? Get instant answers now!

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

z = 2 ± 19 3

Got questions? Get instant answers now!

( [link] ) 2 m 2 = 5 m

m = 0 , 5 2

Got questions? Get instant answers now!

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

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

x = 3 ± 17

Got questions? Get instant answers now!

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

x = 7 ± 145 4

Got questions? Get instant answers now!

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

11 and 13 or 11 and 13

Got questions? Get instant answers now!

( [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

Got questions? Get instant answers now!

( [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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

( [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

Got questions? Get instant answers now!

Questions & Answers

start new n questions too
Emmaunella Reply
summarize halerambos & holbon
David Reply
the Three stages of Auguste Comte
Clementina Reply
what are agents of socialization
Antonio Reply
sociology of education
Nuhu Reply
definition of sociology of education
Nuhu
definition of sociology of education
Emmaunella
what is culture
Abdulrahim Reply
shared beliefs, values, and practices
AI-Robot
What are the two type of scientific method
ogunniran Reply
I'm willing to join you
Aceng Reply
what are the scientific method of sociology
Man
what is socialization
ogunniran Reply
the process wherein people come to understand societal norms and expectations, to accept society's beliefs, and to be aware of societal values
AI-Robot
scientific method in doing research
ogunniran
defimition of sickness in afica
Anita
Cosmology
ogunniran
Hmmm
ogunniran
list and explain the terms that found in society
REMMY Reply
list and explain the terms that found in society
Mukhtar
what are the agents of socialization
Antonio
Family Peer group Institution
Abdulwajud
I mean the definition
Antonio
ways of perceived deviance indifferent society
Naomi Reply
reasons of joining groups
SAM
to bring development to the nation at large
Hyellafiya
entails of consultative and consensus building from others
Gadama
World first Sociologist?
Abu
What is evolutionary model
Muhammad Reply
Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u
faruk
what are the modern trends in religious behaviours
Selekeye Reply
what are social norms
Daniel Reply
shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society
Lucius
that is how i understood it
Lucius
examples of societal norms
Diamond
Discuss the characteristics of the research located within positivist and the interpretivist paradigm
Tariro Reply
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask