Question

A ball 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?

Answer 1

D. the h coordinate of the vertex is the balls maximum height

Answer 2

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

Explanation:

The height of a ball represents by the function

`h(t) = -4.9t2 + 9.8t + 15`

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

`f(x)=ax^2+bx+c`

then vertex of the function is

`Vertex=(-(b)/(2a),f(-(b)/(2a)))`

In the given function,
`a=-4.9,b=9.8,c=15`.

`-(b)/(2a)=-(9.8)/(2(-4.9))=1`

Substitute t=1 in the given function.

`h(1) = -4.9(1)2 + 9.8(1) + 15=19.9`

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

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