Question

the height of the rocket above ground is modelled by the quadratic function h(t)= -4t^2 + 32t, where h(t) is the height in metres, t seconds after the rocket was launched. How long will the rocket be in the air? how do you know? so the vertex is (4,64) the rocket is at it's maximum point in the air only after four seconds. therefore, is it correct to say that the rocket is in the air for a total of 8 seconds since that is when it is on the ground again?

Answer 1

Correct.

Given ,h(t)= -4t^2 + 32t, where h(t) is the height in metres, t seconds after the rocket was launched.

The rocket will be in the air till it reaches the ground.

So we need to find the time taken for the rocket to reach the ground.

To find time taken for the rocket to reach the maximum point we use formula

t = $\frac{-b}{2a}$

From the given equation , a= -4 and b= 32

Plug in the values in the formula

so t = $\frac{-32}{2(-4)}$= 4 seconds

Hence time taken to reach the maximum height is 4 seconds and it will take another 4 seconds to reach the ground.

Therefore, the rocket will be in the air for 8 seconds.

Answer 2

Yes, this is because this graph is symmetrical. You can also work this out by putting the height as equal to 0 and then solving for t (0 = -4t^2 + 32t)