This experiment was interesting. It required coordination between throwing the object, marking the positions quickly, and accurately measuring the distances. my points are: (0,0) (2,1) (4,0), with (0,0) being the staring point.
create a quadratic equation using the data points
To create a quadratic equation, we can use the general form of a quadratic equation:
y = ax^2 + bx + c
Substituting the data points into the equation, we get the following system of equations:
0 = a(0)^2 + b(0) + c
1 = a(2)^2 + b(2) + c
0 = a(4)^2 + b(4) + c
Simplifying, we get:
c = 0
4a + 2b + c = 1
16a + 4b + c = 0
Substitute c = 0 into the second equation:
4a + 2b = 1
Substitute c = 0 into the third equation:
16a + 4b = 0
4a + b = 0
b = -4a
Substitute b = -4a into the second equation:
4a + 2(-4a) = 1
4a - 8a = 1
-4a = 1
a = -1/4
Substitute a = -1/4 into b = -4a:
b = -4(-1/4) = 1
Therefore, the quadratic equation using the data points is:
y = -1/4x^2 + x