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:
[tex]0 = -16(x^2-8x-9)[/tex]
We can divide by -16, nothing will happen because 0 divided by anything is 0:
[tex]0 = x^2-8x-9[/tex]
To factor any trinomial in standard form (given below), we must find two numbers that add to "b" and multiply to "c":
[tex]0 = ax^2 + bx + c[/tex]
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:
[tex]0 = (x-9)(x+1)[/tex]
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."
