The height of a flare is h, given in metres. The function for height of flare with respect to time t, given in seconds.

Question

The height of a flare is represented by h, given in metres. The function for the height of a flare with respect to time t, given in seconds, after the flare was fired from a boat, can be modeled by the function

 

h (t) = -5.25(t-4)² + 86

 

What was its height when it was fired?

What was the maximum height of the flare?

What was the time when the flare reached its maximum height?

How many seconds after it was fired did the flare hit the water?

Answer 1

To find the height when it was first fired, evaluate h(0).

 

To find the maximum height, look at the k value in the vertex form.   k=86

 

To find the time the flare reached its maximum height, look at the h value in the vertex form.  h=4

 

To find out when the flare hit the water, set h(t) equal to zero and solve for t.  You want to use the greater value of t.