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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

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
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emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
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fine, how about you?
Mohammed
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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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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