The height of a soccer ball that is kicked from the ground can be approximated by the function y=-16x^2 +32x where y is the height of the soccer ball on feet x seconds after it is kicked. Graph this function. find the soccer balls maximum height, and the time it takes the soccer ball to return to the ground. How would you graph this?

Answer 1

I will assume you are not taking Calculus, but have studied the quadratic function, and know how to complete the square

y = -16(x^2 - 2x)
= -16(x^2 - 2x + 1 - 1)
= -16( (x-1)^2 - 1)
= -16(x-1)^2 + 16

so the vertex is (1,16)
suggesting that the max height is 16 after 1 second
so it takes 1 second to up and 1 second to come back down, for a total of 2 seconds for the ball to hit the ground again.

graph?
make a table of values of x and y
and plot

http://www.wolframalpha.com/input/?i=plot+y%3D-16x%5E2+%2B32x