Question

The function f(x) = −x2 − 4x + 5 shows the relationship between the vertical distance of a diver from a pool's surface f(x), in feet, and the horizontal distance x, in feet, of a diver from the diving board. What is a zero of f(x), and what does it represent?

x = 1; the diver hits the water 1 foot away horizontally from the board
x = 1; the diver jumps in the pool at 1 foot per second
x = 5; the diver hits the water 5 feet horizontally from the board
x = 5; the diver jumps in the pool at 5 feet per second

Answer 1

The answer is the first option, which is:
`x=1` the diver hits the water
`1 foot` away horizontally from the board.

The explanation for this problem is shown below:

1. You have the following quadratic equation given in the problem above:

`image`

3. To find the zeros, you can factor the quadratic function,as following:

`f(x)=-(x-1)(x+5)=0\\ x=1; x=-5`

4. You must take the positive value of
`x`, which is the horizontal distance from the board to the surface of the pool hitted by the diver.