Question

The function f(x) = −x^2 − 5x + 50 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?

A. x = 5; the diver jumps in the pool at 5 feet per second
B. x = 10; the diver jumps in the pool at 10 feet per second
C. x = 10; the diver hits the water 10 feet horizontally from the board
D. x = 5; the diver hits the water 5 feet away horizontally from the board

Answer 1

We will solve the equation to find a zero of f(x):
`-x^(2)-5x+50=0`
The formula is:
`x_(12) = \frac{-b\pm \sqrt{b^(2)-4ac } }{2a}`where:
a=-1, b=-5, c =50
`x_(12) = (5\pm √(25+200) )/(-2)= (5\pm √(225) )/(-2)= (-10)/(-2)=5`This is the only solution because the other is:
`(5+10)/(-2)= (15)/(-2)=-7.5`which is not possible.
Answer: D) The diver hits the water 5 feet away horizontally from the board.