The function y=-0.03x^2+1.60x models the path of a kicked soccer ball. The height is y, the distance is x, and the units are meters. How far does the soccer ball travel? How high does the soccer ball go? Describe a reasonable domain and range for the function.
Are all domains and ranges reasonable for real-world situations? Explain.

Question

The function y=-0.03x^2+1.60x models the path of a kicked soccer ball. The height is y, the distance is x, and the units are meters. How far does the soccer ball travel? How high does the soccer ball go? Describe a reasonable domain and range for the function.
Are all domains and ranges reasonable for real-world situations? Explain.

anonymous · Answer

to get how far the the ball goes, plug 0 in for y
0 = -0.03x^2+1.60x 
0 = x (-0.03x + 1.60)
(x = 0 which is not the solution) or x = 1.60/0.03 = 53.33m

the maxium height of the ball is when x = -b/(2a) = -1.60 / (2*-0.03) = 26.67. Evaluating at x = 26.67 gives max height to be 21.33 m