RWA #1 Unit: M Concepts: 4-6 Conic Sections

1. Parabola- the set of all points equidistant from a given point, known as the focus and a given line, known as the directrix. 

2. -The formula for parabolas is: (x - h)^2 = 4p(y - k) or (y - k)^2 = 4p(x - h)


- In parabolas, the distance from the focus to the vertex, and the vertex to the directrix is known as 'p' this distance determines whether the parabola will be fat or skinny. In a parabola, the distance from the focus is the same for any given point. 'P' is also known as the focus.
"The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point on the axis of symmetry that intersects the parabola is called the "vertex", and it is the point where the curvature is greatest." (http://en.wikipedia.org/wiki/Parabola)
3. The picture above shows us where the vertex is located on the parabola, and the video also explains the other parts of the parabola and what their functions are.
- One of the most common uses of parabolas in the real world are roller coasters.They provide entertainment at amusement parks. Usually the roller coaster makes use of the outside of the parabola rather than the inside in order to be safer, the engineers have to be sure that the parabola is created well because is not, then it would not be safe.
As we can see int he picture below, there is a central support column which is where the vertex would be on a graph. There are only a couple supports because of the fact that because in parabolas the distance is the same from any point to the vertex, this means that if the engineers can create support columns in main parts of the roller coaster, then the parts that aren't supported by columns would be safe because the weight would be distributed equally.

4. Works Cited Page

• https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhvUoSGMbXCs7QfRZpJXFcLZexCyNN_4m3N6PR2ffMCfUey4Q6R1PwBsLfc9AQwMhI7IYQqYGbLh3cxiU75eDxIwZw1hpNrfVCxUc_YNgDfJfGF0sAVU5mH9bS6T-9fNVmDI9_eoL7CZXI/s1600/Screen+shot+2012-05-08+at+1.37.57+PM.png
• https://blogger.googleusercontent.com/img/proxy/AVvXsEi8RkhF1jy4qFSi00Iv5A3INwo1BwYS92aOT4o32L_eDFf1FjMSGJxcxjF5x9Xt18uci0vxnXKhnO5f93h6i8XytctCKRQ7ycr6KtUCIavZhlJuKTABOv6lMeYEv2-Fdi0jWjuRD25qfN9jyeBz1iXFZ6USitHwlGqCt2uHkNIIxv7Y_POTodU=
• http://mathforum.org/mathimages/index.php/Parabola
• http://youtube.com/parabolasdetailsections/