Question

Armando kicks a football into the air the equation f(x)=-6x^2+38x+0.25 models the height of the football from the ground, in feet, with respect to the Time x, In seconds. Us a graph or a table to estimate the time for the ball to return to the ground after being kicked.

Answer 1

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:

$f(x)=-6x^{2}+38x+0.25$

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:

$-6x^{2}+38x+0.25=0\\\\x = \frac{ -38 \pm \sqrt{38^2 - 4(-6)(0.25)}}{ 2(-6) }\\\\x = \frac{ -38 \pm \sqrt{1444 - -6}}{ -12 }\\\\x = \frac{ -38 \pm \sqrt{1450}}{ -12 }\\\\x = \frac{ 19}{ 6 } + \frac{ 5\sqrt{58}\, }{ 12 }\\\\x = 6.33991$

Thus, the time for the ball to return to the ground after being kicked is 6.34 seconds.