Model 2 : Throw an object up model. Imagine that I am outside and I threw up the

Question

Model 2 : Throw an object up model. Imagine that I am outside and I threw up the object up. Maybe at 1.0 second the ball had a maximum height of 20 feet. Answer the questions that below. 1. 2. 3. 4. 5. Write the equation of the object in vertex form. Assuming that I let go of the object at t-0, what was the object's initial height? Expand the vertex form into standard form to tell me the initial velocity (it is the b-term) When does the object hit the ground? What is the model's domain and range?

Explanation / Answer

the vertex of the equation is

( 1 ,20 )

so , we can write vertex form as

f(t) = -(t-1)^2 + 20

2) plugging t = 0 in the equation

f(t) = -(0-1)^2 + 20

= 19

initial height was 19 feet

3) expanding the vertex form

f(t) = -(t^2 - 2t + 1) + 20

f(t) = -t^2 +2t + 19

initla velocity = 2 feet / second

4) object will hit the ground when height will be 0

-t^2 + 2t + 19 = 0

t = 5.472

object will hit the ground after 5.47 seconds

5) domain is [ 0 , 5.47 )

range is [ 0 , 20 ]

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