SOLUTION: 1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o represents the initial velocity in ft/sec and s^o represents the initial height in feet. A)

Question 161504: 1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o represents the initial velocity in ft/sec and s^o represents the initial height in feet.
A) If a rock is thrown upward what an initial velocity of 64 feet per second from the top of a 25-foot building, write the height (S) equation using this information.
I got s=-16t^2+64t+25
B) How high is the rock after 1 second?
I got s=-16*1^2+64*1+25 so s=73
The questions I need the help on is C)& D)
C) After how many seconds will the graph reach maximum height?
D) What is the maximim height?

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: I'm replacing "s" with "y" and "t" with "x" to get the equation

To answers questions C and D, we need to find the vertex. Remember, the vertex represents the highest/lowest point.

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

.

Since the vertex is

, this means that and .

So at 2 seconds, the object is at the highest point of 89 feet.

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