Please use a pencil and paper for this multi-part question. Please use as few words as possible. You will upload a picture of the graph of this function in another question. An adventurous girl jumped off of a cliff into the ocean while vacationing with friends. Her height as a function of time is modeled by the function: h(t) = −16t2 +16t + 192 where t represents time in seconds, and h is the height in feet. What form is the function written in?

What feature(s) of the function's graph does this form reveal?

What does the feature you named represent in this problem?

Write the function in factored form.

What features of the function's graph does factored form reveal?

In this problem, what do the solutions represent? Why does one of the solutions not make sense?

Write the equation in vertex form.

What feature(s) of the function's graph does vertex form reveal?

In the context of this problem, what does the vertex represent?

What is the output when the input is 2?

What does your answer represent in the context of this problem?

What is the input when the output is 96?

What does your answer represent in the context of this problem?

What is the domain of this function? Think about this scenario - what is x? You may use words or inequality notation.

What is the range of this function? Think about this scenario - what is y? You may use words or inequality notation.​