Question

The function f(x) = −x^2 − 5x + 50 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 = 5; the diver jumps in the pool at 5 feet per second
x = 10; the diver jumps in the pool at 10 feet per second
x = 10; the diver hits the water 10 feet horizontally from the board
x = 5; the diver hits the water 5 feet away horizontally from the board

Answer 1

x = 5; the diver hits the water 5 feet away horizontally from the board

Explanation:

Answer 2

Set the function to equal zero:


`-x^2 - 5x + 50 = 0`

To find the zeros, or solutions, to this problem, we will use the quadratic formula:


`x=(-b\pm√(b^2-4ac))/(2a)`

Plug the values into the equation:


`a = -1, b = -5, c = 50`


`x=(5\pm√(-5^2-4(-1)(50)))/(2(-1))`


`x=(5\pm√(25+200))/(-2)`


`x=(5\pm15)/(-2)`

Solve for both plus and minus:


`(5 + 15)/(-2) = (20)/(-2) = -10`


`(5 - 15)/(-2) = (-10)/(-2) = 5`


`x = -10, x = 5`

The question cannot use a negative value for x, as the diver cannot dive a negative distance from the board.

The answer is 'x = 5; the diver hits the water 5 feet away horizontally from the board', because x represents the horizontal distance away from the board.