Now this is confusing :(

1) the height, h metres, of a model rocket above the ground t seconds after launching is given by the equation h= 4t(50-t) for 0 < t < 50
a) sketch the graph of the rocket's flight.
b) find the height of the rocket when it is launched
c) what is the greatest height the rocket reaches?
d) after how long does the rocket reach the greatest height?
e) how long is the rocket in the air?

2) a farmer decides to fence a new rectangular paddock with the greatest possible area, using an existing fence for one side and 40 metres of fencing to make the other three sides. let the area of the paddock be defined as A m^2
a) write an equation using x and y to describe the area of the paddock
b) write an equation using x and y to describe the length of the new fence
c) rearrange the equation so that y is the subject
d) substitute this value of y into the equation for the area
e) using the intercept method find the coordinates of the turning point

thanks in advance

1a) well i cant sketch it here but i can tell you where your intercepts should be :)
your normal graph would have the axis x and y but in this case, your x axis will be t and your y axis will be h
h intercept occurs when t = 0
h= 4(0)(50-0)
h = 0

t inercept occurs when h = 0
0= 4t(50-t)
using the null factor law:
4t = 0 or 50 - t = 0
t = 0 or t = -50

the t co-ordinate for the turning point will be half way between the t intercepts
t = -50/2
t = -25
when t = -25,
h = 4(-25)(50+25)
h = -1575
turning point at (-25, -1575)
this means your graph is a minimum (looks like a smiley face)

HOWEVER the question states that the domain is 0 < t < 50
therefore, the graph must be restricted to t values between 0 and 50
to do this, multiple all values by -1
therefore,
h intercept = 0
t intercepts = 0 or 50
turning point is at (25, 1575)
your sketch should therefore represent a maximum graph (sad face) to model the motion of a rocket as it flies into the hair and comes back down