this thread will be better when we get more math people on it. Saint-Phoenix is a math major. I haven't had to deal with focus points so I'm not the best person to address them.
Lol no I am far from math god. I don't really know the answer to the first question. I kind of understand it more or less but can't explain it in its entirety.
Here Azarah. All points on the parabola are equidistant from the focus. You can see that from this picture. Knowing the focus is relatively useless for understanding how to graph the function though. It probably has practical uses in the real world that you won't ever see unless you get a job working with it and have some sort of math degree.
I've never had to do that so e-how will tell you. 1 of 5 Measure the distance across the top of the parabola from one side to the other, and measure the depth of the parabola. 2 of 5 Divide the distance across the parabola by two to find the radius. For example, if the parabola has a diameter of 26 inches, you would divide 26 by two to get a radius of 13 inches. 3 of 5 Square the parabola radius. For example, if the parabola has a 13 inch radius, you would square 13 to get 169. 4 of 5 Multiply the depth of the parabola by 4. For example, if the parabola was 5 inches deep, you would multiply 5 by 4 to get 20. 5 of 5 Divide the Step 3 result by the Step 4 result to find the distance above the vertex where the focal point is located. In this example, you would divide 169 by 20 to find the focal point is 8.45 inches above the vertex.
Ohhhhhhhhh lol I think I know how to do this. The internet for some reason gives these other steps Ok (x-h)^2=4p(y-k) (h,k) is the center P is the focal point
You can find the vertex by setting the equation =0 and finding the x values for which the equation equals zero. If you get two x values (from factoring or quadratic formula) then the average of both of those x values is the x value for your vertex. Plug that in the main equation to find the y coordinate for the vertex.