Question

In the quadratic function f(d) = -0.6dxd + 5.4d + 0.8 where d is the horizontal distance that a ball travels in yards, and f(d) is the height, in yards, of the ball at d horizontal yards. What would be the total horizontal distance the ball travels while in the air?

Answer 1

Answer:

Horizontal distance, d = 9.146

Step-by-step explanation:

The given function is

$f(d) = -0.6d^{2} + 5.4d + 0.8$

The horizontal distance, d, is the distance on ground. So, set f(d) = 0.

That is, a height of zero which becomes the ground level.

$0 = -0.6d^{2} + 5.4d + 0.8$

Using the quadratic formula:

$d = \frac{-5.4±\sqrt{5.4^{2} -4(-0.6)(0.8)} }{2(-0.6)}\\ \\d = \frac{-5.4±\sqrt{29.16 + 1.92} }{-1.2}\\\\d = \frac{-5.4±\sqrt{31.08} }{-1.2} = d = \frac{-5.4±5.57}{-1.2}\\\\d = -0.146, 9.146$

Thus, the ball is in air between d=-0.146 to d=9.146.

Since the distance can not be negative, the ball remains in the air between d = 0 to d = 9.146.

Therefore d = 9.146