Question

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.

Answer 1

8 ft

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

Answer 2

8 ft

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