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 $x_{12} = \frac{5\pm \sqrt{25+200} }{-2}= \frac{5\pm \sqrt{225} }{-2}= \frac{-10}{-2}=5$This is the only solution because the other is:$\frac{5+10}{-2}= \frac{15}{-2}=-7.5$which is not possible.
Answer: D) The diver hits the water 5 feet away horizontally from the board.