How to find the quadratic equation of best fit for five points in the shape of a parabola?

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MathLover112358

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Hi this is my first time posting so I apologise if I post to the wrong place or have done something incorrectly.

I have recently started a maths task where I have dropped a paper whirlybird (a rotating helicopter like piece of paper) and measured the time taken for it fall when modifying wing length. I have five different points and when plotted they seem to make the shape of a parabola. I am note sure how to go about finding the equation with 5 different points. I know with three points you can use simultaneous equations to solve the equation but with this I don't know where to even begin. Also it doesn't form a perfect parabola it only resembles one.

Any suggestions are welcome :)
 
Assuming you are not required to do this by hand, but just need the results for your project, you can enter the data into Excel and make a "trendline", which includes the option of using a quadratic (or other polynomial) fit.

But also, the fact that it looks like a parabola to you doesn't necessarily mean that that is the most appropriate form to fit. Ideally, you would want to have a theoretical reason to expect a certain form, and fit it to that; but Excel will give you an R-squared value telling you how good a fit it is, and you can compare the graph visually to see how it looks. More data would give you more certainty.

It might be interesting to show us the data and your formula, so we could offer opinions as to whether what you are doing makes sense.
 
You do a multiple linear regression on x and x^2, treating them as different variables.

With only five data points, you will not get a highly reliable estimate.
 
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