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Introduction to quadratic inequalities.

The first part of this assignment is brought to you by our unit on functions . In fact, this part is entirely recycled from that unit.

The following graph shows the temperature throughout the month of March. Actually, I just made this graph up—the numbers do not actually reflect the temperature throughout the month of March. We’re just pretending, OK?

A graph that shows the temperature throughout the month of March
  • On what days was the temperature exactly 0 ° size 12{0 rSup { size 8{ circ } } } {} C?
  • On what days was the temperature below freezing?
  • On what days was the temperature above freezing?
  • What is the domain of this graph?
  • During what time periods was the temperature going up?
  • During what time periods was the temperature going down?
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The following graph represents the graph y = f ( x ) size 12{y=f \( x \) } {} .

A graph of f(x).
  • Is it a function? Why or why not?
  • What are the zeros?
  • For what x size 12{x} {} -values is it positive?
  • For what x size 12{x} {} -values is it negative?
  • Draw the graph y = f ( x ) 2 size 12{y=f \( x \) - 2} {} .
  • Draw the graph y = f ( x ) size 12{y= - f \( x \) } {}
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OK, your memory is now officially refreshed, right? You remember how to look at a graph and see when it is zero, when it is below zero, and when it is above zero.

Now we get to the actual “quadratic inequalities” part. But the good news is, there is nothing new here! First you will graph the function (you already know how to do that). Then you will identify the region(s) where the graph is positive, or negative (you already know how to do that).

x 2 + 8x + 15 > 0 size 12{x rSup { size 8{2} } +8x+"15">0} {}

  • Draw a quick sketch of the graph by finding the zeros, and noting whether the function opens up or down.
  • Now, the inequality asks when that function is> 0 size 12{>0} {} —that is, when it is positive. Based on your graph, for what x size 12{x} {} -values is the function positive?
  • Based on your answer to part (b), choose one x size 12{x} {} -value for which the inequality should hold, and one for which it should not . Check to make sure they both do what they should.
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A flying fish jumps from the surface of the water with an initial speed of 4 feet/sec.

  • Write the equation of motion for this fish.
  • Find the zeros of the graph, and graph it.
  • Based on your graph, answer the question: during what time interval was the fish above the water?
  • During what time interval was the fish below the water?
  • At what time(s) was the fish exactly at the level of the water?
  • What is the maximum height the fish reached in its jump?
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Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
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Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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