Do you know the quadratic formula?
If h(t) = 75, then to find t, solve 75 = -5t^2+50t , for t. It's a quadratic equation, so there are two answers.
So I have a function: h(t)=-5t^2+50t, and this is supposed to model the flight path/time of a firework going off at the Sydney Harbour Bridge.. H(t) is the height in metres, and t is the time in seconds.
We have a whole sheet based on this problem, and I can do most of it... There was one task where we had to say at which height the firework is after 3 seconds, and I think it was 105 metres.
The turning point is at (5,125), and the x-intercepts are (0,0) and (10,0).
Anyway, the task which is really doing my head in is something along the lines of this (I don't have the sheet with me right now): "In order to make the fireworks show safe for everybody, it is important that the rockets are at least 75m above the heads of the audience (i.e. h(t)=75. At which point should the fireworks operator set off the fuse?" And then we had three options, can't remember all of them, but one of them was "Between 6 and 8 seconds".
Oh, and there was another one saying "If the operator wants the fireworks to go for three seconds longer, how would this affect the turning point?"
Could you please tell me how to go about solving these problems? Would be greatly appreciated!!