Amir 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), x
seconds after Amir threw it, is modeled by h(x)=-(x+1)(x-7), left parenthesis, x, right parenthesis, equals, minus, left parenthesis, x, plus, 1, right parenthesis, left parenthesis, x, minus, 7, right parenthesis How many seconds after being thrown will the ball reach its maximum height?
We need to find where the maximum i. The maximum or minimum is at the vertex. We know where the zero are because the equation is written in the zero form
We know the vertex is 1/2 way between the zeros
h(x)=-(x+1)(x-7)
Using the zero product property
x+1 = 0 x-7 =0
The zeros are at -1 and 7
Adding the two together and dividing by 2
(-1+7)/2 = 6/2 =3
The maximum is at 3. We know it is the maximum because the equation is pointing down because of the negative out front.
