A national park visitor left a trail near the top of a waterfall to get a better look at the falls. Against the complaints of her hiking companion, she started tossing rocks over the edge onto the trail at the bottom of the falls, 92 feet below. Just then, a park ranger arrived at the scene. The ranger cited the park visitor for climbing over a guard rail as well as endangering the lives of people on the path below by throwing rocks. The park visitor argued that they are small rocks and she wasn’t throwing them hard enough to hurt anyone.

The following table gives the height of the rock above the path at the base of the falls for the first 0.80 seconds of its flight (data was collected using a Texas Instruments Calculator Based Laboratory). Time is given in seconds after the rock was thrown, and height is given in feet above the ground.
Create a model for the data analytically. In other words, find the quadratic model using the vertex you identified in Part a), one other data point from the table, and the vertex form of a quadratic function. Show your work (using paper and pencil). Embed a picture of your work and your quadratic model as your response to Part b).