Here's that other question. (I'm not trying to get anyone to do the work for me, it's just that the 3 questions are due tomorrow and I'm like this ...)

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A warning flare is fired vertically from the top of a tower. It's height h in metres after t is given by the equation h = 10 + 40t - 5t²

A) how high is the tower

*For this I substituted t for 0(zero) and got an answer of 10m.

B) what height is reached by the flare.

*For this I "completed the square" and got "h=-5(t-4)² + 78"...don't know if that's right of what to do after*

C) how long is it in the air (until it hits the ground)

I have no idea here

Originally Posted by tdotodot
Here's that other question. (I'm not trying to get anyone to do the work for me, it's just that the 3 questions are due tomorrow and I'm like this ...)

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A warning flare is fired vertically from the top of a tower. It's height h in metres after t is given by the equation h = 10 + 40t - 5t²

A) how high is the tower

*For this I substituted t for 0(zero) and got an answer of 10m.
Assuming that the flare was fired at t= 0, yes. That's a reasonable assumption but the problem should have said something like "in metres t seconds after firing".

B) what height is reached by the flare.

*For this I "completed the square" and got "h=-5(t-4)² + 78"...don't know if that's right of what to do after*
It's easy enough to check: $\displaystyle (t- 4)^2= t^2- 8t+ 16$ so $\displaystyle -5(t-4)^2= -5t^2+ 40t- 80$ and $\displaystyle -5(t-4)^+ 78= -5t^2- 40t- 2$. No, that's not the same thing as $\displaystyle 10+ 40t- 5t^2$.
$\displaystyle 10+ 40t- 5t^2= 10- 5(t^2- 8t)= 10- 5(t^2- 8t+ 16- 16)= 10- 5(t- 4)^2+ 80= 90- 5(t- 4)^2$

Now you know, I hope, that a square is never negative so $\displaystyle -5(t-4)^2$ is never positive and the height is always less than to equal to its value when t= 4.

C) how long is it in the air (until it hits the ground)

I have no idea here
In your answer to a, you said that the tower was 10 metres above the ground since h(0)= 10.
That means you are taking h= 0 at the ground. Solve the equation $\displaystyle 10+ 40t- t^2= 0$