91.8k views
2 votes
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?

User James Ehly
by
7.5k points

2 Answers

4 votes

Answer:

9 seconds

Explanation:

saaaample

User Robert Stevens
by
8.9k points
4 votes
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."
User Skwny
by
8.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories