Marble roll to find -kx²/r² + k parabolic quadratic equation
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-r
r
k
1. Place this paper on an incline. Starting below the x-axis, roll a marble up and across the the y-axis.
When you roll the marble, ensure that the y-axis is the axis of symmetry.
Repeat until you get a consistently repeatable arc. Sketch the arc. Roll the marble on the arc to confirm your path is correct.
2. Measure the distance from the y-axis to one x-axis intercept on the x-axis. This is the distance r.
3. Measure the distance from the x-axis to the y-axis intercept. This is k.
4. Find the function for the path of the marble.
Things to think about:
The shape is a parabola, so the function must be f(x) = ax² + bx + c
(you might think about why that must be the function)
What is c?
What does the axis of symmetry tell you about b?
Can you solve what remains to get a?
y-axis
x-axis