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.

Question

Mathematics

Kylie

24 February, 20:52

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.

+4

Answers (1)

Know the Answer?

Kendall Mcneil · Answer 1

A zero of a function is the value of x when the function equals zero.

Here, when f (x) = 0

0 = - x^2 - 7x + 30

x^2 + 7x - 30 = 0

x^2 - 3x + 10x - 30 = 0

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

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

x + 10 = 0 or x - 3 = 0

x = - 10 or x = 3

but the horizontal distance cannot be zero,

therefore, x = 3 and it means that the diver hits the water 3 feet away horizontally from the board.