Question

A model rocket is shot straight up into the air. The table shows its height, h(t), at time t. Graph the table below and determine a function, in standard form, that estimates the height of the rocket at any given time.
Time(s) Height (m)
0 0.0
1 25.1
2 40.4
3 45.9
4 41.6
5 27.5
6 3.6
I graphed it and there is only one x intercept which is (0,0) and the vertex is (3, 45.9) im having trouble determining a function in standard form

Answer 1

clearly there is an x-intercept somewhere just beyond 6. See how the height is descending.

Since the given h values do not show an obvious symmetry, it is not immediately clear where the vertex is.

However, since h(0) = 0, if

h(t) = at^2 + bt + c

c = 0, so

h(t) = at^2 + bt
Plugging in t=1 and t=2, we have

a+b = 25.1
4a+2b = 40.4
a = -4.9, b=30

h(t) = 30t - 4.9t^2

So, the other t-intercept is at t = 6.12

Answer 2

So what is the vertex?

Answer 3

Huh? You said above what the vertex is.

as always, it is at t = -b/2a

It is not at t=3, but very close. Probably good enough.