The function f (x) = - x2 - 9x + 10 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 = 1; the diver jumps in the pool at 1 foot per second

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

C: x = 1; the diver hits the water 1 foot away horizontally from the board

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

Question

Mathematics

Dominick Suarez

19 March, 02:40

The function f (x) = - x2 - 9x + 10 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 = 1; the diver jumps in the pool at 1 foot per second

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

C: x = 1; the diver hits the water 1 foot away horizontally from the board

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

+3

Answers (1)

Know the Answer?

Elaine · Answer 1

Answer

C: x = 1; the diver hits the water 1 foot away horizontally from the board

Explanation

The question requires you to solve for x.

f (x) = - x² - 9x + 10

When f (x) = 0

-x² - 9x + 10 = 0

= x²+9x-10 = 0

The product in this expression is - 10

The factors of this expression is 9

Factors are 10 and - 1.

x²+9x-10 = x²-1x+10x-10 = 0

=x (x-1) + 10 (x-1) = 0

= (x+10) (x-1) = 0

This means that;

x+10=0 or x-1=0

x = - 10 x = 1.

Since distance can not be negative, x = 1.