Question

A ball is thrown straight up from a cliff. The function f(x) = –4.9t2 + 17t + 19 describes the height of the ball, in meters, as a function of time, t, in seconds. What is the maximum height of the ball? At what time is that height reached? Round your answers to 1 decimal place.

Maximum height:

__ meters


Time:

__ seconds

Answer 1

Maximum height: 33.7 meters

Time: 1.7 seconds

Explanation:

Suppose we have a quadratic equation in the following format:

`f(t) = at^(2) + bt + c`

In a is negative, the maximum point of the function happens at the time of

`t_(v) = -(b)/(2a)`

And it's value is:
`f(t_(v))`

In this question:

`f(t) = -4.9t^(2) + 17t + 19`

So
`a = -4.9, b = 17, c = 19`

The time of the maximum height is:

`t_(v) = -(b)/(2a) = -(17)/(2*(-4.9)) = 1.7`

The maximum height is:

`f(1.7) = -4.9*(1.7)^(2) + 17*1.7 + 19 = 33.7`