Letter to Next Year's Math Analysis Students

It will be fine.... :)

        Math Analysis is just a fancy name for pre-calculus but do not worry it will be fine. If throughout the whole year you follow some simple guidelines then your year be more successful and yes you will pass. The first thing towards having a successful year in this class is to be free to try something new. It is a flipped classroom and although it might seem like a crazy thing to do always from the very beginning be open minded to try it. It never hurts. Mrs. Kirch will most likely tell you some few tips at the beginning of the year and I would pay very close attention to them and make sure to follow them. Whenever Mrs. Kirch gives out an assignment make sure that you understand the directions and know what you are doing. Also it is important that you keep up with the work daily and do not fall behind.if you fall behind by one assignment you are left in a bad track. With that being said : Do Not Procastinate! Also everyday come prepared to class and be ready to discuss what was learned the previous day and to work. When watching the videos it is very important that you FITCH: Focus, Involved in process, Tabs closed, Cell Phones away, and Headphones in.  So remember to always FICTH whenever watching the videos. The last and most important thing to follow and in doing so you will definitely succeed in Math analysis is following KIRCH.

  Keep Mrs. Kicrh happy  -  Initiate communictaion( online or in person) -  Remain Honest  -Complete all

                                                                                       assignemnts    -           Have a Positive Attitude                            

       Welcome to the flipped classroom. At first it might seem overwhelming all you have to do is take it one step at a time. When I first came to class I thought I would not be able to adjust to the flipped classroom and I thought I would not be able to use all this technology. There was no specific way that I adjusted to the flipped classroom but just that as the days went by I just sort of adapted to the new setting. During the first few days I was very open-minded about the whole new system and was willing to give it a try. I think that this helped me a lot to come to get used to the flipped classroom. Also all the videos that Mrs. Kirch made to help us with the technology were very helpful and they really did help me become familiar with the technology used in this class.

       From other math classes the main difference in this class is that it is flipped. Instead of the teacher teaching a lesson to the class, students watch the lesson online  through video lessons.  At home students watch the lesson videos, do the WSQ's, and come up with a question for the teacher and peers. At school, students do a group discussion regarding the concept learned the previous night. Apart from all of this there are extra assignments given to students. This class involves the use of technology throughout many assignments. Something that is new in this class is that students create their own blog and throughout the year they post things up. Also students have to create video playlists and create their own student problems. The flipped classroom is very different to a traditional classroom but I think that is a fun experience to go though and I really enjoyed.

Unit V Big Questions

Where does the formula for the difference quotient come from? 

• The Difference Quotient represents a formula which tells us the slope of a line that is tangent to any point on any given graph. In calculus we call this the "derivative"-->The derivative is the slope of the tangent line to a graph f(x). 
• In order to calculate the slope of the tangent line we use the difference quotient.

 So how is the difference quotient derived? Watch the video and find out! :)




Here are some pictures to further visualize :

Citations: 

http://www.analyzemath.com/calculus/Differentiation/difference_quotient.html
http://en.wikipedia.org/wiki/Numerical_differentiation

Unit U Big Questions

Unit U Big Questions

1.) What is continuity? What is discontinuity? 

Continuity means continuous. That means that when we draw a function we are able to draw it without lifting our pencil from the paper. In other words a a function does not have any breaks, no jumps. and no holes. This is how it is defined in calculus. The following functions are continuous:

Discontinuity refers to when a function is not continuous. This means there are jumps, breaks, or holes in the function. In calculus there are 3 types of discontinuities broken down into families. The two families are:

1. Removable discontinuities :     - Point discontinuity (aka a Hole) ; if f(x) has a hole this would be known as a point discontinuity  
2. Non-Removable Discontinuities:      - Jump discontinuity; if a function has a break or snap it is called jump discontinuity                                                         

                                                                     - Oscillating Behavior; a very wiggly function
                                                                     - Infinite Discontinuity ( aka unbounded behavior and occurs                          where there is a vertical asymptote)
 
               

2.) Limits

    What is a limit?

                        - A limit is the intended height of a function. As we go along the X-axis closer and closer to a a certain value, the graph f(x) gets closer to a value on the Y-axis. This y-value is referred to as the limit which is the intended height. 

   When does a limit exist? When does a limit not exist? What is the difference between a limit and a value? 

                 * watch the video and find out :)

                                                                                       
3.) How do we evaluate limits numerically, graphically, and algebraically?  

• Numerically means on a table. So we evaluate limits numerically using an x and y table. We know that a limit is when x approaches a certain value from the left and from the right. So to do the table we put the number that it is approaching in the center and values from the left and from the right the the table below: 
  
• Graphically means looking at a graph. For this we plug in the f(x) equation into the graphing calculator and we use the given picture of the graph. We can identify wherever there are any discontinuities and in doing so we can evaluate the limits just as the picture below:
  
• Algebraically means solving using algebra skills. To do this there are three methods as our options. We have direct substitution, dividing out, and rationalized. The first method we use for all functions is direct substitution. This means we simply plug in the value x is approaching into the function equation and the result is our limit. If we ever get a numerical answer then we are done. If we get a 0 as our answer then we are also done. However if we get  and undefined value then the limit does not exist and if we get 0/0 then this is indeterminate form which means we have to use another method. 

Citations:
http://www.analyzemath.com/calculus/continuity/continuous_functions.html

http://thetwomeatmeal.wordpress.com/2010/11/04/continuous-maps-and-homeomorphisms/

Unit T Big Question # 2

How do the graphs of sine and cosine relate to each of the others? 

a.) Tangent
b.)Cotangent
---The video will go over tangent and cotangent:



c.) Secant: Secant is the reciprocal of cosine. In order to graph the secant  graph we need to graph the cosine graph. Although cosine graphs do not have asymptotes secant graphs do so once we have draw the regular cosine graph we will then draw the asypmtotes for the secant graph. Secant is 1 / cos so the asymptote lies where cos is zero which is at pi/2 and 3 pi/2. So when we do draw the cosine graph with the secant asypmtotes the graph will look like this:

Now the only thing left to do is to draw the secant graph. Again secant is the reciprocal of cosine so its graph it going to be mirrored from it but as we do this we have to remember that the asymptotes are the barriers to our graph:(secant is represented by the green)

d.)Cosecant: For cosecant we follow the same concepts of that of cosine. First we draw the sine graph one a regular unit circle scale. Although sine does not have an asymptote, cosecant graphs do. Cosecant is 1/sin so whenever sine equals 0 there will be an asymptote since it will be undefined. This happens at 0, pi, and 2pi. So when we draw the sine graph with the cosecant asymptotes the graph will look like this:

Now the draw cosecant we see that there are two sets asymptotes so two graphs will be drawn. Again since  cosecant is the inverse of sine then the cosecant graph will be a reflection of the sine graph. Now when doing so we have to take two things into consideration:

                           *the sine graph was divided into two sections because of the asymptoes so that means there will be one cosecant graph in between each of the asymptotes for a total of two cosecant graphs. 

                         *Between 0 and pi cosecant is positive so the graph has to be reflected above the x-axis and cosecant is negative between pi and 2 pi so the graph needs to be reflected below the x-axis. 

The graph ends up looking like this:

                                                    

Citations for images:

http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphtrigfunctions.html
http://www.intmath.com/trigonometric-graphs/1-graphs-sine-cosine-amplitude.php

Unit T Big Question # 3

Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill? 

• Looking at the Unit Circle and ASTC, we see that tangent is positive in the first quadrant, negative in the second, positive in the third, and negative in the fourth. Now if we take the unit circle and make it so that it is on a graph it would be like this: 

Tangent is sine over cosine and we know that there is an asymptote whenever the value is undefined. Since tangent is sin/cos then the value will be undefined whenever cosine equals zero and that happens at pi/2 and 3 pi/2. 

                                                 pi/2 ( 0, 1) -------- y/x= 1/0=undefined

                                                 3 pi/2 (0,-1)-------y/x= -1/0= undefined

So we have an asymptote at pi/ 2 and 3 pi/2 which is represented by the picture below:

Now that we have the asymptotes we have the barrier to each graph. So we had said that tangent is positive in the first quadrant so that means that between 0 and pi/2 the tangent curve will be going up above the x-axis towards the asymptotes but not touching it. Between pi/2 and pi tangent is negative so the curve will be below the x-axis going up towards the asymptote. If we do this for all the quadrants we get a result of the following graph, which shoes the final tangent graph:

* This is why the tangent graph goes up and it is really based on the placement of the asymptotes that guide how we draw tangent graphs. 

• For cotangent the same process is taken to explain why cotangent graphs are downhill.

 Looking at the unit circle cotangent is positive in the first quadrant, negative in the second, positive in the third, and negative in the fourth. So again like tangent we draw the unit circle on a plane. This type however cotangent is cosine over sine. So this time the asymptotes will lie whenever x/y is undefined.This only happens at pi and 0 or 2 pi.

                                               pi ( -1,0)------x/y= -1/0 = undefined

                                              0 / 2 pi (1,0)------x/y= 1/0= undefined 

*So we have asymptotes at pi and 0 and 2 pi. 

Now we set our barriers we can draw the graph. Between 0 and pi/2 cotangent is positive so it will be above the x-axis only this time the curve will be going down because the it is framed by the asymptote. We do this for all the quadrants and in result get the following graph,which shows the final cotangent graph:

Citations for images:

http://www.biology.arizona.edu/biomath/tutorials/trigonometric/graphtrigfunctions.html

http://demo.activemath.org/ActiveMath2/search/show.cmd?id=mbase://LeAM_calculus/curves/ex_cot_pole

Unit T Big Question # 4

Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? 

Watch the video and find out why!! :D

Unit T-Big Question #1

How do the trig graphs relate to the Unit Circle.?

a.) Period? Why is the period for sine and cosine 2pi, whereas the period for tangent and cotangent is pi?

Trig graphs are clycical, meaning that they repeat themselves over and over gain. One time through this cycle is called a period. Looking at the Unit Circle we can divide into four quadrants in which each particular quadrant has certain trig functions that are positive or negative depending n the quadrant. We represent this by ASTC, like the picture below.:
                                 

-Sine: Looking at sine we see that sine is positive in the first quadrant, positive in the second quadrant, negative in the third, and negative in the third. In result, the pattern for sine is +, +, -, -. so we see that for the pattern to repeat itself again we have to go through one whole cycle around the unit circle thus 2pi since the untie circle is 2pi all the way around. The following picture shows how the pattern looks like on the unit circle:

-Cosine: Looking at cosine we see that it is positive in the first quadrant, negative in the second, negative in the third, and positive in the fourth. The pattern is +,-, -, +. Like sine we see that it takes one whole cycle around the unit circle for the pattern of cosine to repeat itself so that is why the period is 2pi. The following picture shows how the pattern looks like on the unit circle:

            *Remember a period is when the pattern starts and end. Because it takes both sine and cosine one whole cycle around the unit circle to repeat themselves the period is 2pi. 

-Tangent/Cotangent: Looking at cotangent and tangent both are positive in the first quadrant, negative in the second, positive in the third, and negative in the fourth. The pattern for cotangent and tangent is +, -, +, -. We can see that it takes half the time of sine and cosine for the pattern of tangent/cotangent to repeat itself. We have +, -, and then again +, -., so the pattern begins to repeat itself half way through the unit circle which is pi. The following picture shows how the pattern looks like on the unit circle:

b.) Amplitude? How does the fact that sine and cosine have amplitudes of one relate to what we know about the Unit Circle?

 --Looking at the Unit Circle we see that the greatest distance we have is one. This puts a limit at to how far the sine and cosine graphs can reach thus making it its amplitude.  The sine of 90 degrees is 1 and the sine of 270 degrees is -1, which further explains that the amplitude is 1. The cosine of 0 degrees is 1 and the cosine of 180 degrees is -1 which again makes the amplitude 1.


citations for images:

http://www.regentsprep.org/Regents/math/algtrig/ATT3/referenceTriangles.htm

http://etc.usf.edu/clipart/galleries/617-unit-circles

Unit S Assessment #3

Unit S Concept 3







What is this about?
A problem is presented from Unit S Concept 3 which is using power-reducing formulas. This video goes over one of the problems from the pq's and goes over s step by step explanation on how to solve it. It shows how a function that has a power of four can be reduced to a function that has a power of one using various identities and formulas. It involves product-to-sum formulas and much more.

What does the viewer need to pay special attention to in order to understand the concept?
- One thing that the viewer need to pay close attention to is how the constant "m" was used and how it was substituted back. There is a lot of simplifying in this problem so it is important to carefully substitute it where it belongs. Just like when we use "M" and then we have to go back and place back in what "m" equals and so on.

- Another important to pay close attention to is the various formulas that were used. While simplifying the problem we see a lot of identities that we can use and go further to plugging it into the formula they correspond to. When doing so it important that the viewer is able to see why the certain formula was used and how it was plugged in.

Unit S Assessment #2

Unit S Assessment 2

How are these the same?
We know that these two are the same because for both problems are the same and we are looking for the same thing in both problems. In both pictures we are solving for the sin, cosine, and tangent for the angle value of 75 degrees only that they are solved in different methods. In the first picture we solved using sum and difference formulas and in the second picture we solved using half-angle formulas. We can also verify that these two are same by plugging in the values and solving using the calculator. We would get the same sine value for both results and so on.

Unit S Assessment #4

Unit S Concept 7

What is this about?

A problem is presented from Unit S concept, which is solving equations with half-angle formulas. This problem goes over solving an a trig equation that contains a half-angle using the half-angle formulas learned in this unit. Knowledge from previous units are needed to solve this problem. Things such as the unit circle values, identities, and extraneous solutions will be dealt with in this problem.

What does the viewer need to pay special attention to in order to understand the concept?

-The viewer need to pay close attention to is to the identities being used in this problem especially the ones reviewed from unit Q and how they are being substituted in. 

- The second thing to keep in mind is that at the beginning of the problem we squared the equation and since we raised the problem it is very important to go back and check for any extraneous solutions. 

Student Problem: Unit R Concept 3

Unit R Concept 3

What is this about?
---A problem is presented from Unit R Concept 3 which is trig of an inverse trig function using sum and difference to prove. This is a Type 2 problem in which we find the value of the expression without using a calculator.  Reference will be made to the unit circle and we will be using prior knowledge from this unit. The picture goes over an example problem and shows how to solve it step by step.

What does the viewer need to play close attention to in order to do the problem correctly?
---One really important to take into consideration when solving this problem is that we have to remember how to undo an inverse function. It is important to remember that the opposite of sin-1 is sin and by multiplying them together we get one.

---Another important thing to remember when solving this is to also take into consideration that when we use quadrant angles from the unit circle there can be some ambiguity. However for this problem since we are given the sign of the one we can easily identify what angle it corresponds to.

Student Problem: Unit R Concept 2

Unit R Concept 2

What is this about?
---A problem is presented from Unit R Concept 2 which is using sum and difference formulas when given values using right triangles. This goes over a problem in which it is worked out step by step. It goes over how to solve for the exact values when the two triangles lie in different quadrants. It then goes over to show how to solve for the sine sum and the tangent difference.

What does the viewer need to play close attention to in order to do the problem correctly?
---One really important thing to pay close attention to is the way and the quadrant the triangle is drawn. It is very important to consider the signs; if it is positive it will go up or right and if it is negative it will go down or left. These values are derived from the trig functions given.

----Another thin to pay close attention to is how to correctly plug it into the tangent difference formula. Sine they are fractions it is okay to use the calculator to have the fraction more simple and then we can continue solving by hand.

Student Problem: Unit R Concept 1

Unit R Concept 1

What is this about?
---A problem is presented from Unit R Concept 1 which is exact values of sums or differences. This problem goes over how to use sum and difference to find the trig functions of sine, cosine, and tangent using the appropriate sum and difference formulas. The problem is worked out step by step and divided into two sections. The top goes over the sum part while the bottom part goes over the difference part.

What does the viewer need to play close attention to in order to do the problem correctly?
---When doing this problem it is important that the reader appropriately writes the correct ordered pair for the "u" and "v" with the correct signs( negative or positive). These ordered pairs come from the unit circle to the angle they correspond.

---Another thing to really pay close attention to s how the tangent part for both parts was solved. When solving for tangent since we are using fraction it can get really confusing. It is important to really show the work in this part and remember that in order to get rid of radicals in the bottom we have to multiply by its conjugate.

Unit Q Concept 4 Problems

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Solving Concept 2 Problems

Concept 2 Problem:

Problem #5 from PQ:   sin (x)= 1/2; cos(x)=radical 3 / 2

Solving it using identities and with right triangles:

Deriving the Pythagorean Identities

Main Pythagorean Identity:
                                     
                                       cos^2 (-) + sin^2 (-) = 1

Taking a Look Back at the Unit Circle:

The Pythagorean theorem states that the square of the long side equals the square of the two other sides added together.
                                 x^2+y^2=1
In the unit circle the longest side is the radius which always equals 1. X is our cosine while Y is our sine. This is how we get:
                                        cos^2 (-) + sin^2 (-) = 1

Deriving the Two Remaining Pythagorean Identities:
The following picture shows how the last two remaining Pythagorean identities are derived.

Reflective Blog Post

1. How have you performed on the Unit O and P tests?  What evidence do you have from your work in the unit that supports your test grade (good or bad)?  Be specific and include a minimum of three pieces of evidence.

RESPOND HERE:
I have performed good in both Unit O and P tests. On Unit O I received an overall score of 98% and in Unit P I received also received an overall score of 98%. For both units I watched all the videos and completed the WSQ. I followed through the videos by writing notes and highlighting important information in the SSS packets of both units. If something is in bold or is repeated within the video I make sure to make a note of it. I also filled all the required problems and for some concepts I did extra problems for extra practice. For unit O I got all eights on my quizzes. For Unit P I got all eights and one seven in my quizzes. What really helped me better prepare for Unit P were the WPP's that we had to do. I also completed the practice test for both Units and i checked my answers. For every answer I got correct I put a check mark next to the problem and if I got the answer incorrect I would fix it.  

2. You are able to learn material in a variety of ways in Math Analysis.  It generally follows this pattern:

→ Your initial source of information is generally the video lessons and SSS packets followed by a processing and reflection activity via the WSQ
→ individual supplemental research online or in the textbook before class
→ reviewing and accessing supplementary resources provided by Mrs. Kirch on the blog
→  discussion with classmates about key concepts
→ practice of math concepts through PQs
→ formatively assessing your progress through concept quizzes
→ cumulatively reviewing material through PTs
→ Final Assessment via Unit Test.

Talk through each of the steps given in the following terms:
a. How seriously do you take this step for your learning?  What evidence do you have to support your claim?  Make sure to make reference to all 8 steps.
b. How could you improve your focus and attention on this step to improve your mastery of the material?  What specific next steps would this entail?  Make sure to make reference to all 8 steps.

RESPOND HERE:
Step 1- I take watching the video lessons and following through with the SSS packets very seriously. It is the number one thing I make sure to do before class the next day. I feel that if I do not watch the videos carefully that I will not understand the concept and be lost for the PQ's. I always watch the videos when they are assigned and as prove I have my SSS packets all filed out with the information covered in the videos and also turn in the WSQ's. I feel that I have done a good job with the video lesson and feel that I should keep it up.  

Step 2- I do not take this step as seriously. I do believe it is important for my learning but I only go in search for additional resources when I am still confused about the concept or need more help. In unit P I was a little lost in concept 6 and so I looked at the extra problems that were online and practiced with those. I could improve my focus more on this step by every night after watching the videos at least looking for an additional website to double check that I have really understood the concept. 

Step 3- Like step two I only take a look at these supplementary resources when I find myself struggling in a concept. It is rare that I really take a look at them.I think that in order to build a bigger focus on this step  I will look at them after finishing the WSQ. I will review some of the resources put up and see how they relate to the concept we are learning. 

Step 4- I do not really take this step very seriously all the time. There are times when my group and I do not even discuss the questions because we discuss something else. It is really easy to get distracted my the group. There are times when only I and one other person discuss the concept while the others are talking. Steps that should be taken to improve this is to first make sure that everyone including myself in the group has their math material out. I will make sure that all the questions get answered and take more command of the group to me truly focused and paying attention.  

Step 5- I take this step very seriously. I am really strict in doing the PQ's. I try to finish them in class. I  check that my answers are correct and when i do not understand I problem I get help form my group. I have the PQ's worked out in my spiral notebook. I can take this step more seriously by making sure I finish all the PQ's before I start on another concept. 

Step 6- I take this step very seriously. I take it very seriously because it s a part of my grade and also because it helps me see how prepared I am to test on that material. When i do not get at least an eight or a seven on a test I retake the quiz to make sure I know how to do it. I could improve my focus on this step by setting a goal to get all eights on the quizzes. 

Step 7- I take this step very seriously as well. I use the PT to test what I know and what I need to review. I try to do the PT as if it was a test. I try to do it without looking at the SS packet and then check my answers and pretend that if it were a test I would receive that score. 

Step 8-  I take this step extremely important. Tests are a really big part of how much I have learned. It is also worth a lot for grades. It is really important to me that I pass all the tests and always strive for an A. The lowest test grade I have received is a B. I prepare myself for the test with the PT.

3. Reflect on your learning this year thus far by considering the following questions:
a.  How confident do you generally feel on the day of a Unit Test?  Give evidence and specifics to back up your answer.
b.  How well do you feel you have learned the math material this year as compared to your previous years in math? Give evidence to support your claim.
c.  How DEEPLY do you feel you have learned the math material this year as compared to your previous years in math?  Give evidence to support your claim.
d.  Do you normally feel like you understand the WHY behind the math and not just the WHAT/HOW?  Meaning, do you understand why things work, how they are connected to each other, etc, and not just the procedures?  Explain your answer in detail and cite specific evidence from this year.
e. How does your work ethic relate to your performance and success?  What is the value of work ethic in real life?

RESPOND HERE:
On the day of the test I generally feel confident. I feel prepared to take tests by the fact that in my quizzes I scored eights most of the time thus making feel like I have understood the concept. The main reason I feel confident on Unit test days is because when I do the PT I act as if that was the test itself. I try to do it all without looking at the SS packets to test what I really have mastered. when I see that I completed most if not all the test by myself, this makes me feel confident for tests. I feel that this year I have really math material more in depth as compared to previous years. I feel like I have become really engaged in my learning this year. In my previous math years I have been used to just learning the material and understanding how to do it for the tests. I never really understood how it was related to other math concepts or how some equations were derived since they were just given. This year I feel like have really engaged myself more in learning the math material since we really focus on why something is the way that it is and how it applies to real life situations. For example, I did not know how the trig functions related to the unit circle but it makes much more sense. I have really come to learn the WHY behind the math. I feel like now I really understand why certain things work the way they work. Last year I learned about the conic sections but only knew how to graph them and find their equation. This year I learned how to explain how they were formed and how they played a role in real life objects. I learned that the focus of the parabolas is what sends sound waves in whisper dishes. I feel that I have a really good work ethic although at times I do feel lazy. I like to make sure that I do my work. When something is assigned I make sure to turn it in on time. I also try to work ahead at times. I fell that my good work ethics is reflected in my tests scores. The lowest grade I have received in a test is a B and I think that has to do in most part of the work that is done. There is a really great value in work ethic in real life. It prepares us for the future. When we have our own careers we will always be working and if we do not develop good working ethics right now we will struggle to create them in the future.

WPP#14: Unit P Concept 7

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WPP #13: Unit P Concept 6

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WPP #12: Unit O Concept 10

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WPP #11

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Deriving the Unit Circle

Deriving The Unit Circle

What is the unit circle? 

            - It is a circle whose radius is ONE

Where does a unit circle come from?

             - A Unit Circle is derived from special rights triangles. Such triangles like 45, 45, 90 or 30,60, 90 degrees triangles. If we we at their rules and properties we can see the relationship they have with the unit circle. 

This video below will go over deriving the Unit Circle:

Conic Sections

Parabolas

1. One of the conic sections formed in a cone is a parabola. The mathematical definition for a parabola is described as the following: the distance from the focus to any point on the graph (parabola) and from that point directly perpendicularly down to the directrix is the same. A parabola is constructed when it has a focus on the inside and the directrix on the outside.The distance from the vertex to the focus is the same  as the distance from the vertex to the directrix and this value is known as "p".  A parabola is created on a cone when it is sliced so that it is cut parallel to the slope of the cone. 

2.  How far the focus is from the vertex of the parabola or how close it is, affects its shape. We determine the distance from the focus to the vertex by the value of "P". "P" tells us how many units away the focus is from the vertex and how skinny or fat the parabola is. If the "P" value is a small number such as a fraction then it will be a narrow parabola. If the "p" value is a big number or anything greater than one then it will open wider. 

3. The properties of parabolas are seen in real life all the time. They are seen in parabolic satellites, parabolic mirrors, parabolas in bridges,the path of a ball, whisper dishes, and much more. In whisper dishes since they are paraboliod shaped so when a person speaks into the speaker which is the focus the other person will hear what is said at the end of the other dish. This is because when the whisper enters the speaker or the focus, the sound waves travel to the other focus because of the angle of the paraboliod is shaped and the focus.Parabolas are also present when using flashlights or car headlights. The properties of the parabola are used to reflect the light rays flowing from the focus of the parabola in parallel rays.   

Citations  

 Parabola image from: http://www.mathwarehouse.com/quadratic/parabola/focus-and-directrix-of-parabola.php
Conic sections video: http://www.youtube.com/watch?v=BnWEI5o35G8