Question

A ball is thrown in the air from a ledge. Its height in feet is represented by  f(x) = –16(x^2 – 5x – 6), where x is the number of seconds since the ball has been thrown. The height of the ball is 0 feet when it hits the ground. How many seconds does it take the ball to reach the ground? As

Answer 1

I believe your answer is 6 seconds.

Because the height of the ball = -16(x² - 5x - 6), when the height of the ball is 0, which is when it is on the ground, we can set -16(x² - 5x - 6) equal to 0. This also allows us to divide by -16, and then we can solve the equation:

x² - 5x - 6 = 0
(x - 6)(x + 1) = 0

So x = 6 or x = -1, and because a quantity of time cannot be negative, x would have to be 6, which means it takes 6 seconds for the ball to reach 0 feet.

I hope this helps!