Question

A rock 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?

Answer 1

9 seconds

Explanation:

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Answer 2

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:

`0 = -16(x^2-8x-9)`

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

`0 = x^2-8x-9`

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

`0 = ax^2 + bx + 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:

`0 = (x-9)(x+1)`

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."