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?

x = 10; the diver hits the water 10 feet away horizontally from the board

x = 3; the diver hits the water 3 feet away horizontally from the board

x = 10; the diver jumps in the pool at 10 feet per second

x = 3; the diver jumps in the pool at 3 feet per second

Question

Mathematics

Hugo Phillips

19 December, 09:33

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?

x = 10; the diver hits the water 10 feet away horizontally from the board

x = 3; the diver hits the water 3 feet away horizontally from the board

x = 10; the diver jumps in the pool at 10 feet per second

x = 3; the diver jumps in the pool at 3 feet per second

+3

Answers (1)

Know the Answer?

India Ellison · Answer 1

Setting f (x) = 0, we have:

-x2 - 7x + 30 = 0

The roots of this quadratic equation are:

x = 3 and - 10

Since the diver is on a diving board, the - 10 is somewhere behind him. We use the root x = 3 since this distance is in front of the board.

Therefore, the answer is:

x = 3; the diver hits the water 3 feet away horizontally from the board