SOLUTION: A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maxi

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maxi      Log On


   

Question 1179625: A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y=-16x^2+228x+71
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
max height will be at vertex

y=-16x%5E2%2B228x%2B71...rewrite in vertex form by completing square

y=%28-16x%5E2%2B228x%29%2B71...factor out -16

y=-16%28x%5E2-%2857%2F4%29x%2Bb%5E2%29-16b%5E2%2B71.......b=%2857%2F4%29%2F2=%2857%2F8%29

y=-16%28x%5E2-%2857%2F4%29x%2B%2857%2F8%29%29-%28-16%2857%2F8%29%5E2%29%2B71

y=-16%28x-57%2F8%29%5E2%2B3249%2F4%2B71

y=-16%28x-57%2F8%29%5E2%2B3533%2F4=> h=57%2F8 and k=3533%2F4

where k=3533%2F4 is y coordinate of the vertex
so, max height is y=3533%2F4 at x+=+57%2F8
to the nearest tenth of a foot: y=883.3



Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the maximum height reached by the rocket, to the nearest tenth of a foot. y=-16x^2+228x+71
I have no idea why this woman loves so much to make these problems so COMPLEX and time-consuming when they don't have to be.

You can use her method of completing the square to get the equation in vertex form, but only if asked to do so. In this case, 

it's TOTALLY UNNECESSARY and a TOTAL waste of time!

The way to do it is: Maximum height is reached when time, or matrix%281%2C3%2C+x%2C+%22=%22%2C+%28-+b%29%2F%282a%29%29, and since highlight_green%28matrix%281%2C3%2C+f%28x%29%2C+%22=%22%2C+-+16x%5E2+%2B+228x+%2B+71%29%29, that maximum 

height, or 

Now, substitute the value of %28-+b%29%2F%282a%29 into the above, to get that MAXIMUM height.

Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.

In this site,  there is a bunch of lessons on a projectile thrown/shot/launched vertically up
    - Introductory lesson on a projectile thrown-shot-launched vertically up
    - Problem on a projectile moving vertically up and down
    - Problem on an arrow shot vertically upward
    - Problem on a ball thrown vertically up from the top of a tower
    - Problem on a toy rocket launched vertically up from a tall platform

Consider these lessons as your textbook,  handbook,  tutorials and  (free of charge)  home teacher.
Read them attentively and learn how to solve this type of problems once and for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic "Projectiles launched/thrown and moving vertically up and dawn".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.