<< Chapter < Page Chapter >> Page >
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?
Got questions? Get instant answers now!

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 \( x \) } {}
Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

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?
Got questions? Get instant answers now!

Questions & Answers

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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
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
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Advanced algebra ii: activities and homework' conversation and receive update notifications?