The basketball shot at the hoop, I think, will not make it into the hoop. As you can see by the graph, after plotting the points of all of the motions of the ball and drawing a line to predict it, the ball is overshooting the basket. Yet, it is possible that the ball may make it in being it cold still be in range of hitting a backboard and bouncing into the basket.
The first line is y=mx+b which corresponds to y=-2x+2. The 1/2 circle equation is x^2+y^2=2^2. That corresponds to y^2=4-x^2 which simplifies to y=the square root of 4-x^2. Finally the parabola equation is y=(x-2)^2. All the equations together to make the graph give you y={ -2x+2 if x is less than or equal to 0; the square root of 4-x^2 if 0 is less than x and x is less than 2; (x-2)^2 if x is greater than or equal to 2.
So that's it and thats how I found the function. In this activity, first I created a graph to chart my functions. First I graphed y=x^2 which graphed a parabola. Then I graphed the inverse function of y=x^2. To inverse the function i had to flip the x's and the y's. This gave me x=y^2 and then I square rooted both sides to give me a +- square root x=y. In order to inverse the graph all I had to do was take that graph and flip it over the line of y=x. The graphs should line up, in which in my case they did, giving the inverse graph of the function. I was truly amazed by the way it was so simple to inverse a function on a graph. I think graphs can have inverses that can have functions because as long as they are not touching/crossing the y axis at more than 1 point, they are still a function.
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AuthorThis is my blog. Everything I do basically gets documented here!!! :D Archives
April 2015
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