My experience tossing the object and finding the three pairs of coordinates was quite straightforward. I simply tossed the object three times at different angles and recorded the position of the object at three different points in its trajectory.
The three pairs of coordinates that I obtained are as follows:
Pair 1: (0, 0), representing the initial position of the object at time zero.
Pair 2: (1, 2), indicating the position of the object after one unit of time.
Pair 3: (2, 4), showing the position of the object after two units of time.
To write the equation of a quadratic function that models the data, I need to find the quadratic equation in the form of y = ax^2 + bx + c. The challenge here is to determine the values of a, b, and c.
Using the first pair of coordinates, (0, 0), we can substitute these values into the equation to obtain c = 0.
Thus, our quadratic equation becomes y = ax^2 + bx.
Next, I will substitute the second pair of coordinates, (1, 2), into the equation:
2 = a(1)^2 + b(1)
2 = a + b
Finally, I will substitute the third pair of coordinates, (2, 4), into the equation:
4 = a(2)^2 + b(2)
4 = 4a + 2b
Now, I have a system of two equations with two variables:
2 = a + b
4 = 4a + 2b
Solving this system, I find that a = 1 and b = 1. Substituting these values back into the equation, we obtain the quadratic function that models the data as y = x^2 + x.
The main challenge in this task was solving the system of equations to find the values of a and b. However, with only three pairs of coordinates, it was relatively simple to solve and determine the equation of the quadratic function.
You now have three pairs of coordinates from the path of the object.Describe your experience tossing the object and finding the three pairs of coordinates. List the three pairs of coordinates. Then use the coordinates to write the equation of a quadratic function that models the data. Show your work and comment on any challenges that you had.
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