Question

Antoine stands on a balcony and throws a ball to his dog, who is at ground level.

Answer 1

Answer: The ball will hit the ground 4 seconds after being thrown.

Step-by-step explanation:

By definition, the ball hits the grounds when the height is zero.

Then, knowing that the Quadratic function that models that situation is:

$h(x)=-2x^2+4x+16$

You can make it equal to zero:

$0=-2x^2+4x+16$

Now you can use the Quadratic formula:

$x=\frac{-b\±\sqrt{b^2-4ac} }{2a}$

In this case you can identify that:

$a=-2\\b=4\\c=16$

Therefore, knowing these values, you can substitute them into the Quadratic formula and then evaluate, in order to find the solution:

$x=\frac{-4\±\sqrt{4^2-4(-2)(16)} }{2(-2)}\\\\x_1=4\\x_2=-2$

Choose the positive solution.

Then, the ball will hit the ground 4 seconds after being thrown.