Question

s(t)=-16x^2+80t+100

Answer 1

\[\large\rm s(t)=-16t^2+80t+100\]What's up Cheyenne? :)
What do you need to do with this function?

Answer 2

This is the problem :
1. A ball is thrown upward from an initial height of 100 ft with an initial velocity of 80 ft per sec. The path of the
ball is modeled by the function:
After how many seconds does the projectile reach its maximum height? What is this maximum height? After how
many seconds will the ball hit the ground?

Answer 3

The shape of the path the ball follows is parabolic.
So the maximum height is going to be located at the `vertex` of the parabola.

Do you remember how to put a parabola into vertex form? :)

Answer 4

no I do not

Answer 5

\[\large\rm -16t^2+80t\qquad\qquad +100\]Ignore the +100 for now.
We want to try and complete the square on the t's.
We'll start by factoring -16 out of each term to get the coefficient off of the squared term.\[\large\rm -16(\color{orangered}{t^2-5t})\qquad\qquad +100\]And now we want to try and complete the square on this orange part.

Answer 6

In case there in any confusion on what I just did:
I divide -16 out of 16t^2, leaving t^2 in the first part of the bracket.
And I divided -16 out of 80 leaving a 5 on the t.
And the -16 is multiplying the outside of the brackets.

Answer 7

So uhhh to complete the square :p let's see...

Answer 8

okay i get the dividing out the -16 part

Answer 9

Let's split the t's into two equal groups, not the squares but the other ones.
\[\large\rm t^2-5t\quad=\quad t^2-2.5t-2.5t\]We can draw a square to show this relationship.
The side length will be t-2.5.