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?

When we graph the function, it has a vertex of (3, 16).

The maximum of the graph is the highest "x" value on the graph which is 3.

Since the maximum is 3, it will take 3 seconds for the ball to reach its maximum height.

A graph will be shown below showing the function and vertex.

Best of Luck!

3 seconds

Step-by-step explanation:

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.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).