Height h in feet 30506 31250 29300 to find the

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Height h in feet 30,506 31,250 29,300 To find the quadratic model, you will be plugging the data into the model . Thetth=a2+b+cdata 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, b and c.Part 1: Write your 3 by 3 system of equations for a, b, and c. Equation 1: 30,506 = 4a + 2b + c Equation 2: 31,250 = 100a + 10b + c Equation 3: 29,300 = 400a + 20b + c
Part 2: Solve this system. Make sure to show your work. We'll start by taking away equation 1 from equation 2 Now we will go through that same process, only with equations 2 & 3 instead.
We now have two new equations that do not have c in them. We will now multiply equation 5 by 8 and then multiply equation 6 by negative 10. Finally, we will add those equations together to eliminate b, so that we can then solve for a. Now if we divide both sides by 1440, we get
Now we will use this value for a in equation number 6 to solve for b Now that we have the value for b, we can use equation 1 to solve for c
This makes the solution set: a = -16 b = 285 c = 30,000 When we input these into the first three equations and they all held their equalities, making this a verified solution set.Part 3: Using your solutions to the system from part 2 to form your quadratic model of the data. f(x) = -16x² + 285x + 30,000Part 4: Find the maximum value of the quadratic function. Make sure to show your work.

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