NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h = -4.9t^2 + 211 t + 150.

(A) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round answer to 2 decimal places)

The rocket splashes down after _____ seconds.

(B) How high above sea-level does the rocket get at its peak? (Round answer to 2 decimal places)

The rocket peaks at ______ meters above sea-level.

Question

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h = -4.9t^2 + 211 t + 150.

(A) Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round answer to 2 decimal places)

The rocket splashes down after _____ seconds.

(B) How high above sea-level does the rocket get at its peak? (Round answer to 2 decimal places)

The rocket peaks at ______ meters above sea-level.

anonymous · Answer

Yeah I'm totally lost here. When the rocket peaks, that is the vertex I believe. Just don't even know where to start here.

anonymous · Answer

Do you know what the discriminant is? Part of the quadratic formula?

anonymous · Answer

So to find t use the quadratic formula
$$t = \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }$$

The x coordinate, you are correct it's the peak meaning vertex, does this ring a bell...$$\frac{ -b }{ 2a }$$

anonymous · Answer

Yes it does. I used the -b/2a to find an number and then plugged it into the original equation. I then used the quadratic formula, which I do know, to get the answer that did work. Which is great, but I don't understand why, I don't know the process.