You throw a ball straight up from a rooftop. The ball misses the rooftop on its way down and eventually strikes the ground. The following data was collected as the ball traveled and

() = ^2 + + models the data.

Time after ball is thrown (sec) Ball's height above the ground (ft)

2 264

5 276

6 216

a. What is the input variable and its units?

b. What is the output variable and its units?

c. Are there any underlying assumptions that should be made about the model?

d. Calculate all of the possible zeros. Within the context of the problem, explain the meaning of values.

e. Calculate the coordinate of the y-intercept. Explain the meaning of this point within the context of the problem.

f. Describe the domain and range appropriate for the context of this situation. Write your final answer using interval notation and appropriate units.

g. Calculate the vertex. Show your work. Interpret the meaning of the vertex in context of the problem.

h. Using a piece of graph paper, and the above information, to provide a detailed sketch of the path of the ball. Be sure to include an appropriate scale, label the axes within the context of the problem, and include all the information from questions d- g.

i. Algebraically, calculate the average rate of change between 1 = 2 and 2 = 4. Explain the meaning of this result within the context of the situation. Be sure to include appropriate units.

j. Algebraically, calculate the equation in slope-intercept form of the secant line that passes through 1 = 2 and 2 = 4.

i. Add this secant line to your graph from part g. (Label the secant line on the graph.)

ii. Is this calculation an over or underestimate? Explain your reasoning