|This picture demonstrates the use of the parabola and how its properties can be used to create monuments|
This video helps in understanding a parabola by first going over the definition. Then by further going into depth in the equal value of the distance from the focus to the vertex. The video then explains the bouncing of distance.
1) The set of all points equal distant to a focus and a special line called the directix (Taken from the video attached to this post)
2) Key features include the standard form, the direction, the vertex, directrix, focus, axis of symmetry, and value of P
The formula for parabola is (x-h)^2=4p(y-k) or (y-k)^2=4p(x-h)
The parabola will vary in direction depending on which variable is squared and the value of P. If x is squared and p is positive the parabola will direct upwards. If P is negative parabola goes down. When y is squared it will go either left or right. While p is positive the parabola goes to the right. While P is negative the parabola goes to the left.
To find the standard form we can take it from the center value which is the vertex. We can also put together certain pieces if we're not given the vertex. The vertex is found between the focus and directrix on the graph and can be taken from our standard form. The direction is determined by the variables and the value of P. To find our directrix we use fvd and go down or up according to the direction and determined by the value of P. The focus is found the same way. The axis of symmetry is found through when using fvd what value that does change when using fvd such as going dvf on the graph the y will stay the same because its moving horizontally. Value of P is found through setting the value in front of the non-squared term equal to 4p.
The focus of a parabola affects the shape in that if the focus is closer to the parabola its smaller. The focus is also the same distance to any point on the parabola from straight to the directrix is the same value. A parabola's eccentricity is equal to one.
The focus x or y value will change accordingly to what other value changes. Such as if the x values change the focus x value will chance. The focus is also in the middle between the vertex on the axis of symmetry. The focus will change in location according to what direction the parabola is facing.
3) Conics of parabolas could be used in many different way in finding the length of bridges, or monuments. Parabolas can be used to determine the waves of satellite dishes in how they the signals are able to bounce back and forth as shown in the video and these signals then bounce towards satellites which receive this signals and project images on television. (Cited from Mrs. Kirch explanation in class)
4) Works cited
- Mrs Kirch lecture
- . http://www.education.com/study-help/article/pre-calculus-help-conic-sections/