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melamori03 [73]
3 years ago
12

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), i

n 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?
x = 5; the diver jumps in the pool at 5 feet per second
x = 10; the diver jumps in the pool at 10 feet per second
x = 10; the diver hits the water 10 feet horizontally from the board
x = 5; the diver hits the water 5 feet away horizontally from the board
Mathematics
1 answer:
pychu [463]3 years ago
4 0
Set the function to equal zero:

-x^2 - 5x + 50 = 0

To find the zeros, or solutions, to this problem, we will use the quadratic formula:

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Plug the values into the equation:

a = -1, b = -5, c = 50

x=\frac{5\pm\sqrt{-5^2-4(-1)(50)}}{2(-1)}

x=\frac{5\pm\sqrt{25+200}}{-2}

x=\frac{5\pm15}{-2}

Solve for both plus and minus:

\frac{5 + 15}{-2} = \frac{20}{-2} = -10

\frac{5 - 15}{-2} = \frac{-10}{-2} = 5

x = -10, x = 5

The question cannot use a negative value for x, as the diver cannot dive a negative distance from the board.

The answer is '<span>x = 5; the diver hits the water 5 feet away horizontally from the board', because x represents the horizontal distance away from the board.</span>
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