part a: 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? part b: solve 2x2 − 9x + 7 = 0 using an appropriate method. show the steps of your work and explain why you chose the method used.

Part A:

 For this case we have the following function:
 f (x) = -x2 - 7x + 30
 Equaling zero we have:
 -x2 - 7x + 30 = 0
 Rewriting:
 x2 + 7x - 30 = 0
 (x + 10) (x-3) = 0
 x1 = -10
 x2 = 3
 We discard the negative root because we look for a dimension (> 0).
 
 a zero of f (x) is:
 x = 3 feet
 It represents the horizontal distance of a diver from the diving board.

 Part B:

 We have the following equation:
 2x2 - 9x + 7 = 0
 Factoring we have:
 (x-1) (2x-7) = 0
 The solutions are:
 x1 = 1
 x2 = 7/2
 
 x1 = 1
 x2 = 7/2
 The method is chosen by the speed in the calculations of the roots.