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), xx seconds after antoine threw it, is modeled by: h(x)=-2x^2+4x+16h(x)=−2x 2 +4x+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.
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.
h(x) = -2x² + 4x + 16
At the time the ball is thrown,
x = 0
h(0) = -2 × 0² + 4 × 0 + 16 =