Question

A soccer ball is kicked from the ground in an arc defined by the function, h(x) = -8x 2 + 64x. At what point does the ball hit the ground?

(0,4)
(0,8)
(4,0)
(8,0)

Answer 1

The soccer ball hit the ground at (8, 0)

Solution:

To find at what point the ball hit the ground we make the given function equal to zero.

Here the given function is
`h(x)=-8 x^(2)+64 x`

We make h(x) = 0 and try to find the value of x

h(x) = 0

`-8 x^(2)+64 x=0`

-8x (x - 8) = 0

-8x = 0 or (x - 8) = 0

Therefore x = 0 or x = 8

At x= 0 the ball was not kicked. Now we try to find the value of the function by substituting x = 8 in the given function and find the value of the function.

`h(8)=-8\left(8^(2)\right)+64(8)`

=-512 + 512 = 0

Thus the ball hit the ground at (8,0).