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?

Answer 1

f(x) is the vertical distance from the diver to the water
the zero is when the diver hits the water
find the value of x that make f(x)=0

0=-x²-9x+10
undistribute -1
0=-1(x²+9x-10)
what 2 numbers multiply to -10 and add to get 9
-1 and 10
0=-1(x+10)(x-1)
set to zero

x+10=0
x=-10, false, you can't go a negative distance

x-1=0
x=1


the zero is at x=1 and it represents when the diver hits the water