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.
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). Answer: 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 Answer: x1 = 1 x2 = 7/2 The method is chosen by the speed in the calculations of the roots.
