This lab will have you look at the parabolic path to

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This lab will have you look at the parabolic path to try to determine the maximum altitude the plane reaches. First, you will work with data given about the parabola to come up with a quadratic model for theflight. Then you will work to find the maximum value of the model. Now for the data:Time (t) in secondsHeight (h) in feet22364520320154033715To find the quadratic model, you will be plugging the data into the model h=at2+bt+c.The data points given are just like x and y values, where the x value is the time tin seconds and the y value is the altitude hin feet. Plug these into the model and you will get equations with a, band c.
Modeling the ProblemPart 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: Plot the parabola. Do this on an online graphing technology and copy and paste the results below. Label the given data plus the maximum point. A good way to start labeling your axes is to have the lowerleft point be (0, 20000)
Part 6: Reflective Writing.Did this project change the way you think about how math can be applied to the real world? Write at least 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 opinionabout applying math. Refer to specific parts or aspects of this project in your reflection. Can you think of any other recreation activities in which math might play an important role?

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