The function f(x) = −x2 − 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?

The zero is x = 5, and it represents that the diver will enter the pool's surface 5 feet in front of the diving board.

Explanation:

The function is f(x) = - x² - 5x + 50.

Where:

f(x) is the vertical distance of a diver from a pool's surface, andx is the horizontal distance of a diver from the diving board.

A zero of f(x) represents a point where the diver is at the surface of the pool. There might be two possible zeros.

Solve the equation to determine the zeros:

- x² - 5x + 50 = 0Multiply both sides by - 1:  x² + 5x - 50Factor: (x + 10) (x - 5) = 0Use zero product property: x + 10 = 0 or x - 5 = 0From x + 10 = 0 you get x = - 10From x - 5 = 0 you get x = 5.The negative zero is not valid as it would be a point behind the diving board, so the meaningful zero is when x = 5, meaning that the diver will touch the surface of the pool at 5 feet in front of the diving board.