The function f(x)=−x2−7x+30 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? A) x = 10; the diver hits the water 10 feet away horizontally from the board. B) x = 3; the diver hits the water 3 feet away horizontally from the board. C) x = 10; the diver jumps in the pool at 10 feet per second. D) x = 3; the diver jumps in the pool at 3 feet per second.

To find the zero of the function f(x) = −x^2 − 7x + 30, we need to determine the value of x that makes f(x) = 0. A zero of f(x) is a solution to the equation −x^2 − 7x + 30 = 0.

Solving the quadratic equation we get:

- (x - 3)(x + 10) = 0

This equation equals zero when either (x - 3) = 0 or (x + 10) = 0. Therefore, we have:

x - 3 = 0 or x + 10 = 0 x = 3 or x = -10

However, a negative distance does not make sense for this scenario since we're talking about the horizontal distance from the diving board, so we can disregard x = -10.

The only practical solution is x = 3. This means that when the diver is 3 feet away horizontally from the diving board (x = 3), the vertical distance from the surface of the pool is 0 (they hit the water).

So the correct answer is: B) x = 3; the diver hits the water 3 feet away horizontally from the board.