Antoine stands on a balcony and throws a ball to his dog, who is at ground level. The ball's height (in meters above the ground), xxx seconds after Antoine threw it, is modeled by: h(x)=-2x^2+4x+16h(x)=−2x 2 +4x+16h, (, x, ), equals, minus, 2, x, squared, plus, 4, x, plus, 16 What is the height of the ball at the time it is thrown?

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:

You can make it equal to zero:

Now you can use the Quadratic formula:

In this case you can identify that:

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

Choose the positive solution.

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