Question

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.

Answer 1

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).
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.