An object is shot/thrown straght up from the ground.
In the absence of air, its height above the gound, in meters,
after t seconds is given by this h function: h(t) = -5t² + 30t
(The 30 indicates an initial speed ("muzzle velocity") of 30 m/s, about 66 MPH)

t	h(t)
0
1
2
3
4
5
6

Solve h(t)=25 (i.e. at what time(s) t is the object's height 25m)    t=
Solve h(t)=10    t=
Solve h(t)=0    t=
Solve h(t)=45    t=

Graph the function. Adjust the viewport so that the curve in quadrant I occupies most of the screen.
What is its maximum point:
What are the x-intercepts of the function:

An object is shot/thrown straght up from the ground.
In the absence of air, its height above the gound, in meters,
after t seconds is given by this h function: h(t) = -5t² + 60t
(The 60 indicates an initial speed of 60 m/s, about 132 MPH). Note this twice the initial speed as the first function.

t	h(t)
0
1
2
3
4
5
6
7
8
9
10
11
12

Solve h(t)=45    t=
Solve h(t)=100    t=
Solve h(t)=0    t=
Solve h(t)=180    t=

Graph the function. Add it to the graph of the first function. Adjust the viewport so that the two curves occupy most of the screen.
What is its maximum point:
What are the x-intercepts of the function:

So doubling the initial velocity the time aloft and the maximum height reached.

The distance, in meters, a dropped object will fall in t seconds
is given by this d function: d(t) = 10t²
(in the absence of air)

t	d(t)
0
1
2
3
4
5
6
7
8
9
10

Empire State Building's 86th floor observatory is 320m (1050') above the street:
Solve d(t)=320    t=
Solve d(t)=640    (twice the height of the ESB, twice the time?)    t=

The height of an object dropped from 1000m above the ground as a function of time t
is given by this h function: h(t) = -5t² + 1000
(assuming no pesky atmosphere)

t	h(t)
0
1
2
3
5
10
11
12
15

When does the object land on the ground?
Solve h(t)=1000    t= (Hasn't fallen any distance)
Solve h(t)=800 (i.e. when is it 800m high, i.e. fallen 200m)    t=
Solve h(t)=500    t= (Halfway to the ground)
Solve h(t)=0    t= (Hit the ground)