Aball is thrown from the top of a hill. the graph shows the relationship between the height h, in meters, of the ball above the ground at the base of the hill and the time t, in seconds, after the ball is thrown. the function h(t) = -4.9t2 + 9.8t + 15 models h as a function of t. what is the significance of the vertex of the parabola in terms of height and/or time?

The maximum height of the ball is 19.9 meters after 1 second.

Step-by-step explanation:

The height of a ball represents by the function

where, h(t) is the height in meters, of the ball above the ground at the base of the hill and the time t, in seconds, after the ball is thrown.

In the given equation leading coefficient is -4.9 which is a negative number. So, it is a downward parabola and vertex of a downward parabola represents the maximum value of the function.

It means vertex of the given function represents the maximum height of the ball.

If a quadratic function is defined as

then vertex of the function is

In the given function, .

Substitute t=1 in the given function.

The vertex of the function is (1,19.9).

Therefore, the maximum height of the ball is 19.9 meters after 1 second.

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,