Answer:
The time for the ball to return to the ground after being kicked is 6.34 seconds.
Step-by-step explanation:
The equation representing the height of the football from the ground (in feet) when Armando kicks the football into the air, with respect to the time x (in seconds) is:
[tex]f(x)=-6x^{2}+38x+0.25[/tex]
Now, when the ball returns to the ground after being kicked, the height is 0 feet.
Compute the value of x for f (x) = 0 as follows:
[tex]-6x^{2}+38x+0.25=0\\\\x = \frac{ -38 \pm \sqrt{38^2 - 4(-6)(0.25)}}{ 2(-6) }\\\\x = \frac{ -38 \pm \sqrt{1444 - -6}}{ -12 }\\\\x = \frac{ -38 \pm \sqrt{1450}}{ -12 }\\\\x = \frac{ 19}{ 6 } + \frac{ 5\sqrt{58}\, }{ 12 }\\\\x = 6.33991[/tex]
Thus, the time for the ball to return to the ground after being kicked is 6.34 seconds.
