# Plane reaches first you will work with data given

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plane reaches. First, you will work with data given about the parabola to come up with a quadratic model for the flight. Then you will work to find the maximum value of the model. Now for the data: Height of a Zero-G Flight t Seconds After Starting a Parabolic Flight Path Time t in seconds 2 10 20 Height h in feet 30,506 31,250 29,300 To find the quadratic model, you will be plugging the data into the model h = at 2 + bt + c . The data points given are just like x and y values, where the x value is the time t in seconds and the y value is the altitude h in feet. Plug these into the model and you will get equations with a, b and c. Part 1: Write your 3 by 3 system of equations for a, b, and c.
Part 2: Solve this system. Make sure to show your work. Part 3: Using your solutions to the system from part 2 to form your quadratic model of the data. Part 4: Find the maximum value of the quadratic function. Make sure to show your work.
Part 5: Sketch the parabola. Label the given data plus the maximum point. A good way to start labeling your axes is to have the lower left point be (0, 25000) Part 6: Reflective Writing. Did this project change the way you think about how math can be applied to the real world? Write one paragraph stating what ideas changed and why. If this project did not change the way you think, write how this project gave further evidence to support your existing opinion about applying math. Be specific.