Question

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

Answer 1

Answer:

the answer is 3.

Step-by-step explanation:

The ball's height is modeled by a quadratic function, whose graph is a parabola.

The maximum height is reached at the vertex.

So in order to find when that happens, we need to find the vertex.

Find the zereos and then divide by 2.

 

Answer 2

Answer:

16 meters

Step-by-step explanation:

The height function is given by:

$h(x)=-(x+1)(x-7)\\h(x)=-(x^2+x-7x-7)\\h(x)=-x^2+6x+7$

The value of x, in seconds, for which the derivate of the height function is zero, is the time at which the maximum height occurs:

$\frac{dh(x)}{dx}= h'(x)=-2x+6=0\\x=3$

For x = 3 seconds, the height is:

$h(3)=-(3^2)+6*3+7\\h(3)=16\ m$

The maximum height that the ball will reach is 16 meters.