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

Answer:

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).