Arock is thrown in the air from the edge of a seaside cliff. its height in feet is represented by f(x) = –16(x^2 – 8x – 9), where x is the number of seconds since the rock was thrown. the height of the rock is 0 feet when it hits the water. how long does it take the rock to hit the water?

Since x is the number of seconds it took the rock to hit the water, x is the value that we are looking for. When the rock hits the water, it's height is 0, therefore, f(x) = 0. So, we can set the expression on the right equal to 0, and solve for 0. Let's do just that:


We can divide by -16, nothing will happen because 0 divided by anything is 0:


To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":


So, for this specific question, let's find two numbers that add to -8 and multiply to 9. These are clearly 9 and -1. We can write it in this way now:


Both answers would be valid, but there can't be negative time, so your answer is "It takes 9 seconds for the rock to reach the water."

The answer to the question is d