SOLUTION: A model rocket is projected straight upward from the ground level according to the height equation h= -16t^2+192t, where t is greater than or = to 0. What is the maxi

Question 286500: A model rocket is projected straight upward from the ground level according to the height equation h= -16t^2+192t, where t is greater than or = to 0. What is the maximum height of the rocket and after how many seconds does the rocket reach maximum height?
I am just somewhat frustrated because it seems as thought the book and my lecture do not have sufficient information to answer this question, and I could really use some help. Thanks.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm using 'x' instead of 't' and 'y' instead of 'h'

The max height will occur at the vertex since the vertex is the highest/lowest point on the parabola. So we must find the vertex.

To find the vertex, we'll use the formula which is the x coordinate of the vertex. Since is in the form where , and , we can plug these values in to get

So the 'x' coordinate of the vertex is . So the highest point occurs when or equivalently when (since I replaced 't' with 'x'). So the rocket reaches the max height at 6 seconds.

From here, just plug into to find the height 'h' at that given 't' value.

Note: the vertex will be (6, h) where 'h' is the height at 6 seconds, but you probably don't need this info.
RELATED QUESTIONS
If a toy rocket launched vertically upward from the ground level, where h is the height... (answered by Alan3354)

Mr. Alim's science class launched a toy rocket from ground level with an initial upward... (answered by solver91311)

A rocket is launched straight up into the air from the ground with an initial speed of 64 (answered by ankor@dixie-net.com)

Harry fires a rocket upward, which travels according to the equation, h(t)=-16t^2+725t... (answered by Alan3354)

This is from a worksheet from Glencoe Algebra 1. Mr Adim's science class launched a toy... (answered by longjonsilver,Earlsdon)

I'm having trouble with this problem: When Victor shoots a model rocket into the air,... (answered by scott8148)

A toy rocket is launched vertically upward from ground level with an initial velocity of... (answered by Boreal)

Tyrone built a model rocket for his science project. The equation h= -16t2+260t models... (answered by josmiceli)

After t sec, the height of a rocket launched straight upward from the ground level with... (answered by ewatrrr)