Question

The function f(x)=-x²+x+12 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? (1 point)
Ox-3; the diver jumps in the pool at 3 feet per second
Ox-3; the diver hits the water 3 feet away, horizontally from the board
Ox-4; the diver hits the water 4 feet away, horizontally from the board
Ox-4; the diver jumps in the pool at 4 feet per second

Answer 1

Explanation:

To find the zero of the function f(x)=-x²+x+12, we set f(x) equal to zero and solve for x:

0 = -x² + x + 12

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = -1, b = 1, and c = 12. Substituting these values into the quadratic formula:

x = (-(1) ± √((1)² - 4(-1)(12))) / (2(-1))

x = (-1 ± √(1 + 48)) / (-2)

x = (-1 ± √49) / (-2)

x = (-1 ± 7) / (-2)

This gives us two possible solutions:

x₁ = (-1 + 7) / (-2) = 6 / (-2) = -3

x₂ = (-1 - 7) / (-2) = -8 / (-2) = 4

Therefore, the zeros of the function f(x) are x = -3 and x = 4.

Now, let's interpret what these zeros represent in the context of the problem. The horizontal distance x represents the distance of the diver from the diving board. Therefore, the zero x = -3 means that the diver hits the water 3 feet away, horizontally from the board. On the other hand, the zero x = 4 means that the diver hits the water 4 feet away, horizontally from the board.

Based on the given function, f(x), the zeros indicate the horizontal distances at which the diver hits the water. So the correct interpretation is:

Ox-3; the diver hits the water 3 feet away, horizontally from the board.