SOLUTION: The height of a ball thrown directly up from a roof 144 ft high with an initial velocity of 128 ft/sec is given by the formula y= 144 + 128t- 16t^2. What is the maximum height atta

Question 215013: The height of a ball thrown directly up from a roof 144 ft high with an initial velocity of 128 ft/sec is given by the formula y= 144 + 128t- 16t^2. What is the maximum height attained by the ball?

At first, the problem looked to be a quadratic equation... but then I assumed it had something to do with the velocity formula. Essentially, I am a bit lost.
Thanks in advance!
-B
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm going to use the variable 'x' instead of 't'.

Start with the given equation.

Rearrange the terms.

In order to find the vertex, we first need to find the x-coordinate of the vertex.

To find the x-coordinate of the vertex, use this formula: .

Start with the given formula.

From , we can see that , , and .

Plug in and .

Multiply 2 and to get .

Divide.

So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also .

Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.

Start with the given equation.

Plug in .

Square to get .

Multiply and to get .

Multiply and to get .

Combine like terms.

So the y-coordinate of the vertex is .

So the vertex is

.

This means that the max height is 400 feet (since the max/min is the y coordinate of the vertex). This max height occurs when (since x=4 at the vertex and I used 'x' instead of 't')

RELATED QUESTIONS
A ball is thrown straight up from the top of a building 128 ft tall with an initial... (answered by ewatrrr)

The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff... (answered by rothauserc)

A ball is thrown vertically upward from the ground with an initial speed of 80 ft/sec.... (answered by funmath)

A ball is thrown vertically upward from the ground with an initial speed of 80 ft/sec.... (answered by stanbon)

A ball is thrown directly upward from a height of 7 ft with an initial velocity of 20... (answered by ikleyn)

A ball is thrown directly upward from a height of 4 ft with an initial velocity of 24... (answered by ikleyn)

If an object is thrown upward from the ground with an initial velocity of 128 ft/sec, its (answered by Alan3354)

An object is thrown from the top of a 144 ft building with an initial velocity of 128 ft... (answered by nerdybill)

A ball is thrown in the air from a height of 4 ft with an initial velocity of 35 ft/sec. (answered by TimothyLamb)