SOLUTION: A rock was thrown upwards off of a seaside cliff and fell down to the beach below. Its motion was described by h = −16t² + 16t +125 where h is the vertical distance above the b

Question 1177208: A rock was thrown upwards off of a seaside cliff and fell down to the beach below.
Its motion was described by h = −16t² + 16t +125 where h is the vertical distance above the beach in meters and t is time after throwing in seconds.

What was the height of the cliff? How can you tell?
How can you tell that the motion of the rock had a maximum height?
Show how to convert the equation in standard form to the vertex form using the method of completing the square.

What was the vertex of the throw?

What was the maximum height of the rock?
How much time had passed since the throw when the maximum height was reached?

When did the rock hit the beach below?

At what time(s) did the rock reach a height of 127m?

At what height was the rock after 2 seconds?

Answer by ikleyn(52786)   (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.

RELATED QUESTIONS
The height of a rock dropped off a 511 foot cliff, h(t), is described by the equation... (answered by jim_thompson5910)

[ A rock is thrown upward from the edge of a cliff. The rock follows the equation below.... (answered by TimothyLamb)

a person standing on the edge of a cliff throws a rock in the air. the path of the rock... (answered by Boreal)

a person standing on the edge of a cliff throws a rock in the air. the path of the rock... (answered by ikleyn)

4. A rock is thrown off a 75-meter-high cliff into some water. The height of the rock... (answered by Boreal)

A rock is thrown upward with a velocity of 12 meters per second from the top of a 32... (answered by rothauserc)

I have a test tomorrow and i need to understand how to work complicated word problems on... (answered by stanbon)

The height s, in feet, of a rock thrown upward at an initial speed of 64 ft/sec from a... (answered by josmiceli)

The height h, in feet, of a stone thrown with an upward speed of 40 ft/s is given by the... (answered by rapaljer)