A soccer ball is kicked and modeled by the function h (x) = -0.0085x²+0.25x+6, where h is the height of the ball in feet and x is the horizontal distance in feet that the ball travels. Find the maximum height of the ball to the nearest foot.

8 ft

Step-by-step explanation:

h (x) = -0.0085x²+0.25x+6,

dh/dx = - 0.017x + 0.35 = 0

x = 0.25 : 0.017

x = 14.7058823529

h (14.7058823529) = - 0.0085 (14.7058823529) ² + 0.25 (14.7058823529) + 6

= 7.8382352941

8 ft

Step-by-step explanation:

h (x) = -0.0085x²+0.25x+6,

The maximum height will be at the vertex

The x coordinate is at

h = - b/2a where b is the x term coefficient and a is the x^2 term coefficient

h = - (.25) / (2 (-.0085)

=14.70588235

We want to find the height so we need to substitute this into the equation

h (14.70588235) = -0.0085 (14.70588235) ^2+0.25 (14.70588235) + 6,

=-1.838235294+3.676470588+6

=7.838235293 ft

To the nearest foot

= 8 ft