Question 204830
h = 1 + 8t - 5t^2.
a) find the height of the cork after 0.8s....i have the answer of 4.2m for this.
Correct.
b) find the time when the cork is at ground level (h = 0)......i have the answer of 1.72s for this.
Correct.
c) explain what the maximum value of t is for which this function is a plausible model for the height of the cork?....i don't understand this question.
hope you can help me by explaining how to do this 
.
By inspection of:
h = 1 + 8t - 5t^2
Rewritten as:
h = -5t^2 + 8t + 1
.
We see that is is a parabola and it opens downward (upside down U).  We can tell by looking at the coefficient associated with the t^2 term (-5) -- since it is negative, think "sad face".  Because of this, we now know that the VERTEX of the parabola is your maximum height/time pair.
There are several ways to find this vertex.
One way is to find the "axis of symmetry"
t = -b/2a = -8/(2(-5)) = -8/(-10) = 8/10 = 4/5 = .8 seconds
.
Height, at that time is:
h = -5t^2 + 8t + 1
h = -5(.8)^2 + 8(.8) + 1
h = 4.2m 
Which is "part a" of this problem.