Question

Alain throws a stone off a bridge into a river below. The stone's height (in meters above the water), X seconds after Alain threw it, is modeled by: h(x) = -5x^2 + 10x + 15. How many seconds after being thrown will the stone hit the water?

A) 1.000 seconds
B) 1.500 seconds
C) 2.000 seconds
D) 2.500 seconds

Answer 1

After setting the quadratic equation h(x) = -5x^2 + 10x + 15 equal to zero and factoring, the solution is x = 3 seconds, indicating the stone hits the water 3 seconds after being thrown.

Step-by-step explanation:

To determine how many seconds after being thrown will the stone hit the water, we need to find the value of x when the height of the stone h(x) is zero, as this represents the stone hitting the water.

The stone's height above the water is given by the equation: h(x) = -5x^2 + 10x + 15. We set this equation equal to zero and solve for x:

0 = -5x^2 + 10x + 15

Factoring the quadratic equation, we divide all terms by -5 for simplification:

0 = x^2 - 2x - 3

Now we factor the equation:

0 = (x - 3)(x + 1)

The solutions to this factored equation are x = 3 and x = -1. Since time cannot be negative, we discard x = -1. Therefore, the stone hits the water 3 seconds after being thrown, which is not one of the options provided. There might be an error in the question or the options given.