The path of a diver diving off a 10-foot platform can be represented by the function h(x) = - 0.5(x^2 - 4x - 21) where h is the diver's height above water and x is the horizontal distance from the platform (in feet). What does the positive zero represent?

x = -3 and 7

Step-by-step explanation:

Given the path of a diver expressed as;

h(x) = - 0.5(x^2 - 4x - 21)

The positive zero occur at when h(x) = 0

Substitue

0  = - 0.5(x^2 - 4x - 21)

-0.5x^2 + 2x + 10.5 = 0

Multiply through by -10

5x^2 - 20x - 105 = 0

x^2 - 4x - 21 = 0

x^2 - 7x+3x - 21 = 0

x(x-7)+3(x-7) = 0

(x+3)(x-7) = 0

x = -3 and 7

Hence the positive zero displacement occurs at x = -3 and 7

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x