SOLUTION: From the top of the building, a ball is thrown straight up with an initial velocity of 128 feet per second. The equation s = −16t2 + 128t + 144 gives the height s of the ball

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Question 1169870: From the top of the building, a ball is thrown straight up with an initial velocity of 128 feet per second. The equation
s = −16t2 + 128t + 144
gives the height s of the ball t seconds after it is thrown. Find the maximum height (in feet) reached by the ball and the time (in seconds) it takes for the ball to hit the ground. (Hint: Let s = 0 and solve for t.)
144 ft
A rectangular building is 144 ft tall.
A curved path starts at the top-right side of the building and goes up and to the right past the right edge of the building. The path gets less steep as it reaches a high point, and then it goes down and to the right, getting steeper as it goes.
The ball is at the end of the path midway between the top of the building and the ground, and its height above the ground is labeled s.
A vertical dashed line starts at the ball and goes down to touch the ground.
1.The maximum height reached by the ball is ? Feet ?

2. The ball hits the ground after 9
seconds. I did figure out number 2 i just need help with the first one
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!

You need the time value when the function value is maximum. Since the function is a quadratic with a negative lead coefficient, the graph is a concave down parabola making the vertex of the parabola the point where the value of the function is a maximum.

For any parabola modeled by an equation of the form , the value of the independent variable ( for your situation) is found by calculating .

Once you know the value of , then calculate the value of

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52788) 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.