In this experiment/project our Survey of College Algebra class used a measurement of a juggle toss to be the example of the measurements of a parabola. To do this just toss a ball from one hand to the other and name a measurement for it.
Oh by the way my name is Danielle, remember me? I have shared my work with you before. So once again you can follow along with my example to learn about parabolas and maybe try this out for yourself so that you may realize how much fun that math can be!
Welcome to a:
My sample toss was 18in x 18in, so all of the following data and formulas are related to this sample. 18in repsents the height or the y value of my toss and 18in across measures the width of my toss or the x value of the juggle toss parabola.
To find the equation of this parabola we used the formula
y = a x^2.
So we just plug in our values of x and y and solve the equation for a. Like this:
18 = a (9^2)
18/81 = a (81/81)
a = 18/81
simplified = 2/9.
Now that we solved for "a" our equation is
y = (2/9) x^2
After we graph the parabola out using that equation we get a parabola graph that looks like this:
This table and graph was made by using our first equation for multiple points by plugging in the x variables of the juggling toss parabola. Also to get the parabola to look like this on the graph we had to turn it upside down. To do that we simply made y a -y and in our case (2/9) changed to (-2/9) and then we add 18 inches to the equation and this brings it above the (0,0) origin and this brings the parabola to flip and just easier to understand when looking at it as a graph.
So the equation then becomes y = (-2/9) x^2 + 18.
To plot the graph I just simply solved for each x and y variable, you can do this by hand or use a program such as Microsoft Excell and create a table and let Excell do all the work for you.
An example of what it will look like if you use the program Micosoft Excell is like the above table and graph.
To find the Arc Length of this parabola or any Parabola click on Danielle's Parabola Arc Length.
This is my class and I with all of our juggling parabolas!
For more information and ideas about working with parabola toss patterns of other dimensions you may link to a page written by one of the following math artists: Danielle, Darlene, Kellie, Jill, Nanyal, Kevin, Crystal, Rachel, Christina, Jennifer, Candice, Vincent Esther and Melinda.