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: 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 [tex]h(x)=-8 x^{2}+64 x[/tex]We make h(x) = 0 and try to find the value of x h(x) = 0 [tex]-8 x^{2}+64 x=0[/tex]-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. [tex]h(8)=-8\left(8^{2}\right)+64(8)[/tex]=-512 + 512  = 0 Thus the ball hit the ground at (8,0).