A toy rocket launched straight up from the ground with an initial velocity of 80ft/s returns to the ground after 5 s.

The height of the rocket t seconds after launch is modeled by the function f(t) = -16t^2+80t

What is the maximum height of the rocket, in feet?
Explain how you found your answer.

Question

A toy rocket launched straight up from the ground with an initial velocity of 80ft/s returns to the ground after 5 s.

The height of the rocket t seconds after launch is modeled by the function f(t) = -16t^2+80t

What is the maximum height of the rocket, in feet?
Explain how you found your answer.

iGreen · Answer

Maximum height is also known as...?

iGreen · Answer

Do you know? @Aureo

Aureo · Answer

Maximum height would be the highest y value

iGreen · Answer

Yes, which is known as what in a parabola?

Aureo · Answer

Ahm.  The vertex?

iGreen · Answer

Yes, and how do we calculate the vertex?

iGreen · Answer

Or more specifically, the x-value for the vertex.

Aureo · Answer

To calculate vertex you do 
$$x=\frac{ -b }{ 2a }$$

iGreen · Answer

Yes, so do it.

$\sf ax^2+bx+c$

iGreen · Answer

So in this case what is 'b' and what is 'a'?

Aureo · Answer

A would be -16 and b would be 80

iGreen · Answer

Yes, so plug them into the formula to find the x-value of the vertex.

Aureo · Answer

Alright.  So it would be -80/-32.  Which = 2.5

iGreen · Answer

Yep, now plug that into the equation to find the y-value, which will be our maximum height.

iGreen · Answer

$\sf f(t)=-16t^2+80t$

$\sf f(2.5)=-16(2.5)^2+80(2.5)$

Btw, this 2.5 represents 2.5 seconds for it to reach the maximum height.

Aureo · Answer

Ahhh. Thank you!

Aureo · Answer

So then

Aureo · Answer

The feet would be 1800?

iGreen · Answer

Check again, I got something different.

iGreen · Answer

@Aureo

Aureo · Answer

Ah.  I squared the wrong one.  It's 100

iGreen · Answer

Yep, max height is 100 ft.

Aureo · Answer

Thank you kind sir

iGreen · Answer

Any time