THE PARABOLA
What sort of function is it |
Type Function-Quadratic function
Examples of ParabolasExamples: y = x2 + 2 , y = -x2 + 2x + 3
Who determined the parabolaBabylonian and Chinese mathematicians first solved quadratic equations by completing the square. They would focus on a length.
How to sketch itFirst create a quadratic function then make a table to represent the coordinates. After you do that draw up a cartesian plane,then plot the points from your table on the plane.
Properties of the FunctionParabola has many properties that are very important. Such as the vertex,focus,axis of symmetry,and directrix. Also any type of rays that are parallel to the axis of symmetry that runs through the centre, would bounce back from the Parabola and to the focus. The vertex is the locus of the focus and directrix.
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Uses in Everyday products
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Parabolas are used in many aspects of everyday life because basically everything is curved. Parabolas are used in satellite dishes, headlights on cars, suspension bridges, a path of an object in air and fountains and also in the McDonald’s M. In Satellite Dishes the radio waves are beamed from the side of the dish to the thingy in the middle. In Headlights the front bit has to be curved to ensure the maximum range of the light. In suspension bridges the cables have to be like a certain parabola angle to prevent the bridge from collapsing or something like that. When you throw an object up into the air it will come back down but it will not come back down at the same angle where it went up but instead it will come back down in the shape of a parabola. The same thing applies to fountains when a jet of water shoots up it comes back down in the shape of a parabola. And the McDonald’s M sign thing that you see in front of every Maccas store in the world is in the shape of a parabola as well. Also like some heaters are curved just like satellite dishes just it isn’t a circle. But it serves the same purpose to direct the rays of heat or whatever to 1 spot on the map. Just like Artillery! Also apparently there are such things as Parabolic mirrors which make you look upside down which i'm pretty sure was just invented for the lols. I really like Parabolas. Don’t you?
How to graph it on Excel
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- First open excel
- Then create a quadratic function(see question 2).
- After that type in x and y underneath each other, x on top.
- Create a table and write any numbers in the row next to x.
- Then apply your function to the numbers next to x to get y.
- Then highlight your table and click on ‘insert’.
- In insert you will see a recommended charts button, in that you will see different graphs.
- Choose whatever graph you want and open it.
- If you are doing a parabola your end result will be a curve if you follow the steps CORRECTLY.
Why do people use Parabolas?
Parabolas are used today in the real world because it helps do things like focusing rays to a certain point by using the angle. Parabolas also magnify light rays by using the angle to spread out the path of the rays. There are also things called parabola skies and the parabolas reduce the turning time. Parabola loudspeakers exist in this galaxy. So parabolas are used to communicate as well.. Also parabolas are used to keep bridges upright so basically parabolas save lives? Hooray for Parabolas. One example is like the “Golden Gate Bridge”, in America. Also parabolas are used to have fun because the path of a rugby ball or soccer ball is a parabola .
How do we use it in everyday lifeParabolas are used in many aspects of everyday life as any lines entering the parabola parallel to its axis will be reflected by the parabolic curve intersect the focus. For example; a parabola is used in satellite dishes where the signal is emitted from the feed horn and then is reflected by the dish (which happens to be a parabola) and the signal travels in quite a narrow beam.
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Who Discovered the Parabola
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Babylonian mathematicians in 1800 BC, left the earliest evidence of the discovery of the quadratic functions on stone tablets. Euclid, a Greek mathematician, also contributed to the discovery of the quadratic function. Brahmagupta, an indian mathematcian, was the first to produce negative solutions with the formula, and Muḥammad ibn Mūsā al-Ḵwārizmī who was a Persian mathematician produced a formula that worked for positive solutions as well. Bhaskara II from India is considered the originator of the function because he basically polished off the equation.
How to sketch it
First create a quadratic function then make a table to represent the coordinates. After you do that draw up a cartesian plane,then plot the points from your table on the plane.
The end
The parabola is a vital part of our lives as it is used in many instances explained in questions 6,7 and 8. A parabola is basically the curve on a graph resulting from a quadratic equation, and in real life, the benefits of the curved surface helps us do many things that we otherwise couldn’t have done. Like keep people from dying on the Golden Gate Bridge cause nobody wants that right?