Question

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

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.